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What is the Least Common Multiple of 7870 and 7888?

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 7870 and 7888 is 31039280.

LCM(7870,7888) = 31039280

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Least Common Multiple of 7870 and 7888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7870 and 7888, than apply into the LCM equation.

GCF(7870,7888) = 2
LCM(7870,7888) = ( 7870 × 7888) / 2
LCM(7870,7888) = 62078560 / 2
LCM(7870,7888) = 31039280

Least Common Multiple (LCM) of 7870 and 7888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7870 and 7888. First we will calculate the prime factors of 7870 and 7888.

Prime Factorization of 7870

Prime factors of 7870 are 2, 5, 787. Prime factorization of 7870 in exponential form is:

7870 = 21 × 51 × 7871

Prime Factorization of 7888

Prime factors of 7888 are 2, 17, 29. Prime factorization of 7888 in exponential form is:

7888 = 24 × 171 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 7870 and 7888.

LCM(7870,7888) = 24 × 51 × 7871 × 171 × 291
LCM(7870,7888) = 31039280