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What is the Least Common Multiple of 478 and 489?

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 478 and 489 is 233742.

LCM(478,489) = 233742

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Least Common Multiple of 478 and 489 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 478 and 489, than apply into the LCM equation.

GCF(478,489) = 1
LCM(478,489) = ( 478 × 489) / 1
LCM(478,489) = 233742 / 1
LCM(478,489) = 233742

Least Common Multiple (LCM) of 478 and 489 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 478 and 489. First we will calculate the prime factors of 478 and 489.

Prime Factorization of 478

Prime factors of 478 are 2, 239. Prime factorization of 478 in exponential form is:

478 = 21 × 2391

Prime Factorization of 489

Prime factors of 489 are 3, 163. Prime factorization of 489 in exponential form is:

489 = 31 × 1631

Now multiplying the highest exponent prime factors to calculate the LCM of 478 and 489.

LCM(478,489) = 21 × 2391 × 31 × 1631
LCM(478,489) = 233742