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What is the Least Common Multiple of 71674 and 71680?

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 71674 and 71680 is 2568796160.

LCM(71674,71680) = 2568796160

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Least Common Multiple of 71674 and 71680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71674 and 71680, than apply into the LCM equation.

GCF(71674,71680) = 2
LCM(71674,71680) = ( 71674 × 71680) / 2
LCM(71674,71680) = 5137592320 / 2
LCM(71674,71680) = 2568796160

Least Common Multiple (LCM) of 71674 and 71680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71674 and 71680. First we will calculate the prime factors of 71674 and 71680.

Prime Factorization of 71674

Prime factors of 71674 are 2, 35837. Prime factorization of 71674 in exponential form is:

71674 = 21 × 358371

Prime Factorization of 71680

Prime factors of 71680 are 2, 5, 7. Prime factorization of 71680 in exponential form is:

71680 = 211 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 71674 and 71680.

LCM(71674,71680) = 211 × 358371 × 51 × 71
LCM(71674,71680) = 2568796160