What is the Least Common Multiple of 55680 and 55692?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 55680 and 55692 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55680 and 55692, than apply into the LCM equation.

GCF(55680,55692) = 12
LCM(55680,55692) = ( 55680 × 55692) / 12
LCM(55680,55692) = 3100930560 / 12
LCM(55680,55692) = 258410880

Least Common Multiple (LCM) of 55680 and 55692 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55680 and 55692. First we will calculate the prime factors of 55680 and 55692.

Prime Factorization of 55680

Prime Factorization of 55692

Now multiplying the highest exponent prime factors to calculate the LCM of 55680 and 55692.

LCM(55680,55692) = 2⁷ × 3² × 5¹ × 29¹ × 7¹ × 13¹ × 17¹
LCM(55680,55692) = 258410880