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What is the Least Common Multiple of 30960 and 30976?

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 30960 and 30976 is 59938560.

LCM(30960,30976) = 59938560

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Least Common Multiple of 30960 and 30976 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30960 and 30976, than apply into the LCM equation.

GCF(30960,30976) = 16
LCM(30960,30976) = ( 30960 × 30976) / 16
LCM(30960,30976) = 959016960 / 16
LCM(30960,30976) = 59938560

Least Common Multiple (LCM) of 30960 and 30976 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30960 and 30976. First we will calculate the prime factors of 30960 and 30976.

Prime Factorization of 30960

Prime factors of 30960 are 2, 3, 5, 43. Prime factorization of 30960 in exponential form is:

30960 = 24 × 32 × 51 × 431

Prime Factorization of 30976

Prime factors of 30976 are 2, 11. Prime factorization of 30976 in exponential form is:

30976 = 28 × 112

Now multiplying the highest exponent prime factors to calculate the LCM of 30960 and 30976.

LCM(30960,30976) = 28 × 32 × 51 × 431 × 112
LCM(30960,30976) = 59938560