Gcd and Lcm Calculator With Steps
With the help of this calculator, you can easily find the greatest common divisor GCD and least common
multiple LCM thanks to the detailed solution. You can find GCD and LCM for two, three and four numbers
Find the greatest common factor of GCD (36; 24)
Solution steps
Way 1
1) Let's find prime factors of numbers. To do this, check whether each of the numbers is prime (if the number is prime, then it cannot be decomposed into prime factors, and it itself is its own decomposition)
36 - composite number
24 - composite number
Decompose the number 36 into its prime factors and highlight them in green. We begin to select a divisor from primes, starting with the smallest prime number 2, until the quotient turns out to be a prime number
36 : 2 = 18 - is divisible by prime 2
18 : 2 = 9 - is divisible by prime 2
9 : 3 = 3 - is divisible by prime 3.
We complete division because 3 is a prime number
Decompose the number 24 into its prime factors and highlight them in green. We begin to select a divisor from primes, starting with the smallest prime number 2, until the quotient turns out to be a prime number
24 : 2 = 12 - is divisible by prime 2
12 : 2 = 6 - is divisible by prime 2
6 : 2 = 3 - is divisible by prime 2.
We complete division because 3 is a prime number
2) Highlight in blue and write out the common factors
36 = 2 ⋅ 2 ⋅ 3 ⋅ 3
24 = 2 ⋅ 2 ⋅ 2 ⋅ 3
Common factors(36 ; 24) : 2, 2, 3
3) Now, to find the GCD, you need to multiply the common factors
Result: GCD (36 ; 24) = 2 ∙ 2 ∙ 3 = 12
Way 2
1) Find all possible divisors of numbers (36 ; 24). To do this, we will one by one divide the number 36 into divisors from 1 to 36, and the number 24 into divisors from 1 to 24. If the number is divisible without a remainder, then the divisor is written into the list of divisors.
For the number 36 we write out all the cases when it is divisible without a remainder:
36 : 1 = 36; 36 : 2 = 18; 36 : 3 = 12; 36 : 4 = 9; 36 : 6 = 6; 36 : 9 = 4; 36 : 12 = 3; 36 : 18 = 2; 36 : 36 = 1;
For the number 24 we write out all the cases when it is divisible without a remainder:
24 : 1 = 24; 24 : 2 = 12; 24 : 3 = 8; 24 : 4 = 6; 24 : 6 = 4; 24 : 8 = 3; 24 : 12 = 2; 24 : 24 = 1;
2) Let's write out all common divisors of numbers (36 ; 24) and highlight in green the largest one, this will be the greatest common divisor of the GCD of numbers (36 ; 24)
Common divisors of numbers (36 ; 24): 1, 2, 3, 4, 6, 12
Result: GCD (36 ; 24) = 12
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Find the least common multiple LCM (52; 49)
Solution steps
Way 1
1) Let's find prime factors of numbers. To do this, check whether each of the numbers is prime (if the number is prime, then it cannot be decomposed into prime factors, and it itself is its own decomposition)
52 - composite number
49 - composite number
Decompose the number 52 into its prime factors and highlight them in green. We begin to select a divisor from primes, starting with the smallest prime number 2, until the quotient turns out to be a prime number
52 : 2 = 26 - is divisible by prime 2
26 : 2 = 13 - is divisible by prime 2.
We complete division because 13 is a prime number
Decompose the number 49 into its prime factors and highlight them in green. We begin to select a divisor from primes, starting with the smallest prime number 2, until the quotient turns out to be a prime number
49 : 7 = 7 - is divisible by prime 7.
We complete division because 7 is a prime number
2) First, we write down the prime factors of the largest number, and then the smallest number. Let's find the missing prime factors. Let's highlight in blue in the list of prime factors of a smaller number, prime factors that are not included in the list of prime factors of a larger number.
52 = 2 ∙ 2 ∙ 13
49 = 7 ∙ 7
3) Now, to find the LCM, you need to multiply the prime factors of a larger number with the prime factors highlighted in blue
LCM (52 ; 49) = 2 ∙ 2 ∙ 13 ∙ 7 ∙ 7 = 2548
Way 2
1) Find all possible multiples (52 ; 49). To do this, we will alternately multiply the number 52 by the numbers from 1 to 49, and the number 49 by the numbers from 1 to 52.
Highlight all multiples 52 in green:
52 ∙ 1 = 52; 52 ∙ 2 = 104; 52 ∙ 3 = 156; 52 ∙ 4 = 208;
52 ∙ 5 = 260; 52 ∙ 6 = 312; 52 ∙ 7 = 364; 52 ∙ 8 = 416;
52 ∙ 9 = 468; 52 ∙ 10 = 520; 52 ∙ 11 = 572; 52 ∙ 12 = 624;
52 ∙ 13 = 676; 52 ∙ 14 = 728; 52 ∙ 15 = 780; 52 ∙ 16 = 832;
52 ∙ 17 = 884; 52 ∙ 18 = 936; 52 ∙ 19 = 988; 52 ∙ 20 = 1040;
52 ∙ 21 = 1092; 52 ∙ 22 = 1144; 52 ∙ 23 = 1196; 52 ∙ 24 = 1248;
52 ∙ 25 = 1300; 52 ∙ 26 = 1352; 52 ∙ 27 = 1404; 52 ∙ 28 = 1456;
52 ∙ 29 = 1508; 52 ∙ 30 = 1560; 52 ∙ 31 = 1612; 52 ∙ 32 = 1664;
52 ∙ 33 = 1716; 52 ∙ 34 = 1768; 52 ∙ 35 = 1820; 52 ∙ 36 = 1872;
52 ∙ 37 = 1924; 52 ∙ 38 = 1976; 52 ∙ 39 = 2028; 52 ∙ 40 = 2080;
52 ∙ 41 = 2132; 52 ∙ 42 = 2184; 52 ∙ 43 = 2236; 52 ∙ 44 = 2288;
52 ∙ 45 = 2340; 52 ∙ 46 = 2392; 52 ∙ 47 = 2444; 52 ∙ 48 = 2496;
52 ∙ 49 = 2548;
Highlight all multiples 49 in green:
49 ∙ 1 = 49; 49 ∙ 2 = 98; 49 ∙ 3 = 147; 49 ∙ 4 = 196;
49 ∙ 5 = 245; 49 ∙ 6 = 294; 49 ∙ 7 = 343; 49 ∙ 8 = 392;
49 ∙ 9 = 441; 49 ∙ 10 = 490; 49 ∙ 11 = 539; 49 ∙ 12 = 588;
49 ∙ 13 = 637; 49 ∙ 14 = 686; 49 ∙ 15 = 735; 49 ∙ 16 = 784;
49 ∙ 17 = 833; 49 ∙ 18 = 882; 49 ∙ 19 = 931; 49 ∙ 20 = 980;
49 ∙ 21 = 1029; 49 ∙ 22 = 1078; 49 ∙ 23 = 1127; 49 ∙ 24 = 1176;
49 ∙ 25 = 1225; 49 ∙ 26 = 1274; 49 ∙ 27 = 1323; 49 ∙ 28 = 1372;
49 ∙ 29 = 1421; 49 ∙ 30 = 1470; 49 ∙ 31 = 1519; 49 ∙ 32 = 1568;
49 ∙ 33 = 1617; 49 ∙ 34 = 1666; 49 ∙ 35 = 1715; 49 ∙ 36 = 1764;
49 ∙ 37 = 1813; 49 ∙ 38 = 1862; 49 ∙ 39 = 1911; 49 ∙ 40 = 1960;
49 ∙ 41 = 2009; 49 ∙ 42 = 2058; 49 ∙ 43 = 2107; 49 ∙ 44 = 2156;
49 ∙ 45 = 2205; 49 ∙ 46 = 2254; 49 ∙ 47 = 2303; 49 ∙ 48 = 2352;
49 ∙ 49 = 2401; 49 ∙ 50 = 2450; 49 ∙ 51 = 2499; 49 ∙ 52 = 2548;
2) Let's write out all common multiples of numbers (52 ; 49) and highlight the smallest in green, this will be the least common multiple of numbers (52 ; 49).
Common multiples(52 ; 49): 2548
Result: LCM (52 ; 49) = 2548
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