What is the Least Common Multiple of 31942 and 31960?
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 31942 and 31960 is 510433160.
LCM(31942,31960) = 510433160
Least Common Multiple of 31942 and 31960 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31942 and 31960, than apply into the LCM equation.
GCF(31942,31960) = 2
LCM(31942,31960) = ( 31942 × 31960) / 2
LCM(31942,31960) = 1020866320 / 2
LCM(31942,31960) = 510433160
Least Common Multiple (LCM) of 31942 and 31960 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31942 and 31960. First we will calculate the prime factors of 31942 and 31960.
Prime Factorization of 31942
Prime factors of 31942 are 2, 15971. Prime factorization of 31942 in exponential form is:
31942 = 21 × 159711
Prime Factorization of 31960
Prime factors of 31960 are 2, 5, 17, 47. Prime factorization of 31960 in exponential form is:
31960 = 23 × 51 × 171 × 471
Now multiplying the highest exponent prime factors to calculate the LCM of 31942 and 31960.
LCM(31942,31960) = 23 × 159711 × 51 × 171 × 471
LCM(31942,31960) = 510433160
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