What is the Least Common Multiple of 854 and 870?
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 854 and 870 is 371490.
LCM(854,870) = 371490
Least Common Multiple of 854 and 870 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 854 and 870, than apply into the LCM equation.
GCF(854,870) = 2
LCM(854,870) = ( 854 × 870) / 2
LCM(854,870) = 742980 / 2
LCM(854,870) = 371490
Least Common Multiple (LCM) of 854 and 870 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 854 and 870. First we will calculate the prime factors of 854 and 870.
Prime Factorization of 854
Prime factors of 854 are 2, 7, 61. Prime factorization of 854 in exponential form is:
854 = 21 × 71 × 611
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
Now multiplying the highest exponent prime factors to calculate the LCM of 854 and 870.
LCM(854,870) = 21 × 71 × 611 × 31 × 51 × 291
LCM(854,870) = 371490
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