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What is the Least Common Multiple of 30960 and 30980?

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 30980 is 47957040.

LCM(30960,30980) = 47957040

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Least Common Multiple of 30960 and 30980 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 30980, than apply into the LCM equation.

GCF(30960,30980) = 20
LCM(30960,30980) = ( 30960 × 30980) / 20
LCM(30960,30980) = 959140800 / 20
LCM(30960,30980) = 47957040

Least Common Multiple (LCM) of 30960 and 30980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30960 and 30980. First we will calculate the prime factors of 30960 and 30980.

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 30980

Prime factors of 30980 are 2, 5, 1549. Prime factorization of 30980 in exponential form is:

30980 = 22 × 51 × 15491

Now multiplying the highest exponent prime factors to calculate the LCM of 30960 and 30980.

LCM(30960,30980) = 24 × 32 × 51 × 431 × 15491
LCM(30960,30980) = 47957040