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What is the Least Common Multiple of 65978 and 65988?

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 65988 is 2176878132.

LCM(65978,65988) = 2176878132

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Least Common Multiple of 65978 and 65988 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 65988, than apply into the LCM equation.

GCF(65978,65988) = 2
LCM(65978,65988) = ( 65978 × 65988) / 2
LCM(65978,65988) = 4353756264 / 2
LCM(65978,65988) = 2176878132

Least Common Multiple (LCM) of 65978 and 65988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65978 and 65988. First we will calculate the prime factors of 65978 and 65988.

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 65988

Prime factors of 65988 are 2, 3, 13, 47. Prime factorization of 65988 in exponential form is:

65988 = 22 × 33 × 131 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 65978 and 65988.

LCM(65978,65988) = 22 × 111 × 29991 × 33 × 131 × 471
LCM(65978,65988) = 2176878132