GCD: 14
GCD: 14
The Greatest Common Divisor (GCD) for 42 56 is 14.
since 14 = 14 x 1 and 56 = 14 x 4 the answer is 14, since it divides evenly into both and clearly nothing larger will.There is a clever algorithm that can help you work this out in the general case:GCD(14, 56) = GCD(14, 56 - 14) = GCD(14, 42)This step (subtract the smaller from the larger) relies on the fact that any number that divides both 14 and 56 also divides 56 - 14.Repeat this:GCD(14, 42) = GCD(14, 42 - 14) = GCD(14, 28)GCD(14, 28) = GCD(14, 28 - 14) = GCD(14, 14)which is clearly 14.This is called Euclid's Algorithm.
GCD(42, 65) = 1
GCD: 21
Greatest Common Divisor (GCD) for 30 42 is 6.
GCD: 6
To find the Least Common Multiple (LCM) of two numbers, you can use the formula LCM(a, b) = (a * b) / GCD(a, b), where GCD is the Greatest Common Divisor. For 14 and 21, the GCD is 7, so the LCM is (14 * 21) / 7 = 42. For 14 and 6, the GCD is 2, so the LCM is (14 * 6) / 2 = 42. Therefore, the LCM of 14 and 21 is 42, and the LCM of 14 and 6 is also 42.
GCD(14, 34) = 2GCD(14, 34) = 2GCD(14, 34) = 2GCD(14, 34) = 2
10
The Greatest Common Divisor (GCD) for 12 14 is 2