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What is the Least Common Multiple of 7546 and 7560?

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 7546 and 7560 is 4074840.

LCM(7546,7560) = 4074840

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Least Common Multiple of 7546 and 7560 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7546 and 7560, than apply into the LCM equation.

GCF(7546,7560) = 14
LCM(7546,7560) = ( 7546 × 7560) / 14
LCM(7546,7560) = 57047760 / 14
LCM(7546,7560) = 4074840

Least Common Multiple (LCM) of 7546 and 7560 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7546 and 7560. First we will calculate the prime factors of 7546 and 7560.

Prime Factorization of 7546

Prime factors of 7546 are 2, 7, 11. Prime factorization of 7546 in exponential form is:

7546 = 21 × 73 × 111

Prime Factorization of 7560

Prime factors of 7560 are 2, 3, 5, 7. Prime factorization of 7560 in exponential form is:

7560 = 23 × 33 × 51 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 7546 and 7560.

LCM(7546,7560) = 23 × 73 × 111 × 33 × 51
LCM(7546,7560) = 4074840