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What is the Least Common Multiple of 55660 and 55680?

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 (LCM) of 55660 and 55680 is 154957440.

LCM(55660,55680) = 154957440

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Least Common Multiple of 55660 and 55680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55660 and 55680, than apply into the LCM equation.

GCF(55660,55680) = 20
LCM(55660,55680) = ( 55660 × 55680) / 20
LCM(55660,55680) = 3099148800 / 20
LCM(55660,55680) = 154957440

Least Common Multiple (LCM) of 55660 and 55680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55660 and 55680. First we will calculate the prime factors of 55660 and 55680.

Prime Factorization of 55660

Prime factors of 55660 are 2, 5, 11, 23. Prime factorization of 55660 in exponential form is:

55660 = 22 × 51 × 112 × 231

Prime Factorization of 55680

Prime factors of 55680 are 2, 3, 5, 29. Prime factorization of 55680 in exponential form is:

55680 = 27 × 31 × 51 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 55660 and 55680.

LCM(55660,55680) = 27 × 51 × 112 × 231 × 31 × 291
LCM(55660,55680) = 154957440