What is the Least Common Multiple of 31804 and 31824?
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 31804 and 31824 is 253032624.
LCM(31804,31824) = 253032624
Least Common Multiple of 31804 and 31824 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31804 and 31824, than apply into the LCM equation.
GCF(31804,31824) = 4
LCM(31804,31824) = ( 31804 × 31824) / 4
LCM(31804,31824) = 1012130496 / 4
LCM(31804,31824) = 253032624
Least Common Multiple (LCM) of 31804 and 31824 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31804 and 31824. First we will calculate the prime factors of 31804 and 31824.
Prime Factorization of 31804
Prime factors of 31804 are 2, 7951. Prime factorization of 31804 in exponential form is:
31804 = 22 × 79511
Prime Factorization of 31824
Prime factors of 31824 are 2, 3, 13, 17. Prime factorization of 31824 in exponential form is:
31824 = 24 × 32 × 131 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 31804 and 31824.
LCM(31804,31824) = 24 × 79511 × 32 × 131 × 171
LCM(31804,31824) = 253032624
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