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What is the Least Common Multiple of 54560 and 54570?

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 54560 and 54570 is 297733920.

LCM(54560,54570) = 297733920

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Least Common Multiple of 54560 and 54570 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54560 and 54570, than apply into the LCM equation.

GCF(54560,54570) = 10
LCM(54560,54570) = ( 54560 × 54570) / 10
LCM(54560,54570) = 2977339200 / 10
LCM(54560,54570) = 297733920

Least Common Multiple (LCM) of 54560 and 54570 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54560 and 54570. First we will calculate the prime factors of 54560 and 54570.

Prime Factorization of 54560

Prime factors of 54560 are 2, 5, 11, 31. Prime factorization of 54560 in exponential form is:

54560 = 25 × 51 × 111 × 311

Prime Factorization of 54570

Prime factors of 54570 are 2, 3, 5, 17, 107. Prime factorization of 54570 in exponential form is:

54570 = 21 × 31 × 51 × 171 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 54560 and 54570.

LCM(54560,54570) = 25 × 51 × 111 × 311 × 31 × 171 × 1071
LCM(54560,54570) = 297733920