What is the Least Common Multiple of 31972 and 31992?
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 31972 and 31992 is 255712056.
LCM(31972,31992) = 255712056
Least Common Multiple of 31972 and 31992 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31972 and 31992, than apply into the LCM equation.
GCF(31972,31992) = 4
LCM(31972,31992) = ( 31972 × 31992) / 4
LCM(31972,31992) = 1022848224 / 4
LCM(31972,31992) = 255712056
Least Common Multiple (LCM) of 31972 and 31992 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31972 and 31992. First we will calculate the prime factors of 31972 and 31992.
Prime Factorization of 31972
Prime factors of 31972 are 2, 7993. Prime factorization of 31972 in exponential form is:
31972 = 22 × 79931
Prime Factorization of 31992
Prime factors of 31992 are 2, 3, 31, 43. Prime factorization of 31992 in exponential form is:
31992 = 23 × 31 × 311 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 31972 and 31992.
LCM(31972,31992) = 23 × 79931 × 31 × 311 × 431
LCM(31972,31992) = 255712056
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