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What is the Least Common Multiple of 462 and 480?

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 462 and 480 is 36960.

LCM(462,480) = 36960

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Least Common Multiple of 462 and 480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 462 and 480, than apply into the LCM equation.

GCF(462,480) = 6
LCM(462,480) = ( 462 × 480) / 6
LCM(462,480) = 221760 / 6
LCM(462,480) = 36960

Least Common Multiple (LCM) of 462 and 480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 462 and 480. First we will calculate the prime factors of 462 and 480.

Prime Factorization of 462

Prime factors of 462 are 2, 3, 7, 11. Prime factorization of 462 in exponential form is:

462 = 21 × 31 × 71 × 111

Prime Factorization of 480

Prime factors of 480 are 2, 3, 5. Prime factorization of 480 in exponential form is:

480 = 25 × 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 462 and 480.

LCM(462,480) = 25 × 31 × 71 × 111 × 51
LCM(462,480) = 36960