What is the Least Common Multiple of 870 and 888?
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 870 and 888 is 128760.
LCM(870,888) = 128760
Least Common Multiple of 870 and 888 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 870 and 888, than apply into the LCM equation.
GCF(870,888) = 6
LCM(870,888) = ( 870 × 888) / 6
LCM(870,888) = 772560 / 6
LCM(870,888) = 128760
Least Common Multiple (LCM) of 870 and 888 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 870 and 888. First we will calculate the prime factors of 870 and 888.
Prime Factorization of 870
Prime factors of 870 are 2, 3, 5, 29. Prime factorization of 870 in exponential form is:
870 = 21 × 31 × 51 × 291
Prime Factorization of 888
Prime factors of 888 are 2, 3, 37. Prime factorization of 888 in exponential form is:
888 = 23 × 31 × 371
Now multiplying the highest exponent prime factors to calculate the LCM of 870 and 888.
LCM(870,888) = 23 × 31 × 51 × 291 × 371
LCM(870,888) = 128760
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