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What is the Least Common Multiple of 65978 and 65984?

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 65978 and 65984 is 2176746176.

LCM(65978,65984) = 2176746176

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Least Common Multiple of 65978 and 65984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65978 and 65984, than apply into the LCM equation.

GCF(65978,65984) = 2
LCM(65978,65984) = ( 65978 × 65984) / 2
LCM(65978,65984) = 4353492352 / 2
LCM(65978,65984) = 2176746176

Least Common Multiple (LCM) of 65978 and 65984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65978 and 65984. First we will calculate the prime factors of 65978 and 65984.

Prime Factorization of 65978

Prime factors of 65978 are 2, 11, 2999. Prime factorization of 65978 in exponential form is:

65978 = 21 × 111 × 29991

Prime Factorization of 65984

Prime factors of 65984 are 2, 1031. Prime factorization of 65984 in exponential form is:

65984 = 26 × 10311

Now multiplying the highest exponent prime factors to calculate the LCM of 65978 and 65984.

LCM(65978,65984) = 26 × 111 × 29991 × 10311
LCM(65978,65984) = 2176746176