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What is the Least Common Multiple of 68460 and 68470?

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 68460 and 68470 is 468745620.

LCM(68460,68470) = 468745620

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Least Common Multiple of 68460 and 68470 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 68460 and 68470, than apply into the LCM equation.

GCF(68460,68470) = 10
LCM(68460,68470) = ( 68460 × 68470) / 10
LCM(68460,68470) = 4687456200 / 10
LCM(68460,68470) = 468745620

Least Common Multiple (LCM) of 68460 and 68470 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 68460 and 68470. First we will calculate the prime factors of 68460 and 68470.

Prime Factorization of 68460

Prime factors of 68460 are 2, 3, 5, 7, 163. Prime factorization of 68460 in exponential form is:

68460 = 22 × 31 × 51 × 71 × 1631

Prime Factorization of 68470

Prime factors of 68470 are 2, 5, 41, 167. Prime factorization of 68470 in exponential form is:

68470 = 21 × 51 × 411 × 1671

Now multiplying the highest exponent prime factors to calculate the LCM of 68460 and 68470.

LCM(68460,68470) = 22 × 31 × 51 × 71 × 1631 × 411 × 1671
LCM(68460,68470) = 468745620