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What is the Least Common Multiple of 3750 and 3760?

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 3750 and 3760 is 1410000.

LCM(3750,3760) = 1410000

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Least Common Multiple of 3750 and 3760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3750 and 3760, than apply into the LCM equation.

GCF(3750,3760) = 10
LCM(3750,3760) = ( 3750 × 3760) / 10
LCM(3750,3760) = 14100000 / 10
LCM(3750,3760) = 1410000

Least Common Multiple (LCM) of 3750 and 3760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3750 and 3760. First we will calculate the prime factors of 3750 and 3760.

Prime Factorization of 3750

Prime factors of 3750 are 2, 3, 5. Prime factorization of 3750 in exponential form is:

3750 = 21 × 31 × 54

Prime Factorization of 3760

Prime factors of 3760 are 2, 5, 47. Prime factorization of 3760 in exponential form is:

3760 = 24 × 51 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 3750 and 3760.

LCM(3750,3760) = 24 × 31 × 54 × 471
LCM(3750,3760) = 1410000