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What is the Least Common Multiple of 55965 and 55984?

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 55965 and 55984 is 3133144560.

LCM(55965,55984) = 3133144560

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Least Common Multiple of 55965 and 55984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55965 and 55984, than apply into the LCM equation.

GCF(55965,55984) = 1
LCM(55965,55984) = ( 55965 × 55984) / 1
LCM(55965,55984) = 3133144560 / 1
LCM(55965,55984) = 3133144560

Least Common Multiple (LCM) of 55965 and 55984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55965 and 55984. First we will calculate the prime factors of 55965 and 55984.

Prime Factorization of 55965

Prime factors of 55965 are 3, 5, 7, 13, 41. Prime factorization of 55965 in exponential form is:

55965 = 31 × 51 × 71 × 131 × 411

Prime Factorization of 55984

Prime factors of 55984 are 2, 3499. Prime factorization of 55984 in exponential form is:

55984 = 24 × 34991

Now multiplying the highest exponent prime factors to calculate the LCM of 55965 and 55984.

LCM(55965,55984) = 31 × 51 × 71 × 131 × 411 × 24 × 34991
LCM(55965,55984) = 3133144560