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What is the Least Common Multiple of 2745 and 2760?

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 2745 and 2760 is 505080.

LCM(2745,2760) = 505080

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Least Common Multiple of 2745 and 2760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2745 and 2760, than apply into the LCM equation.

GCF(2745,2760) = 15
LCM(2745,2760) = ( 2745 × 2760) / 15
LCM(2745,2760) = 7576200 / 15
LCM(2745,2760) = 505080

Least Common Multiple (LCM) of 2745 and 2760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2745 and 2760. First we will calculate the prime factors of 2745 and 2760.

Prime Factorization of 2745

Prime factors of 2745 are 3, 5, 61. Prime factorization of 2745 in exponential form is:

2745 = 32 × 51 × 611

Prime Factorization of 2760

Prime factors of 2760 are 2, 3, 5, 23. Prime factorization of 2760 in exponential form is:

2760 = 23 × 31 × 51 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 2745 and 2760.

LCM(2745,2760) = 32 × 51 × 611 × 23 × 231
LCM(2745,2760) = 505080