What is the Least Common Multiple of 32010 and 32014?
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 32010 and 32014 is 512384070.
LCM(32010,32014) = 512384070
Least Common Multiple of 32010 and 32014 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32010 and 32014, than apply into the LCM equation.
GCF(32010,32014) = 2
LCM(32010,32014) = ( 32010 × 32014) / 2
LCM(32010,32014) = 1024768140 / 2
LCM(32010,32014) = 512384070
Least Common Multiple (LCM) of 32010 and 32014 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 32010 and 32014. First we will calculate the prime factors of 32010 and 32014.
Prime Factorization of 32010
Prime factors of 32010 are 2, 3, 5, 11, 97. Prime factorization of 32010 in exponential form is:
32010 = 21 × 31 × 51 × 111 × 971
Prime Factorization of 32014
Prime factors of 32014 are 2, 16007. Prime factorization of 32014 in exponential form is:
32014 = 21 × 160071
Now multiplying the highest exponent prime factors to calculate the LCM of 32010 and 32014.
LCM(32010,32014) = 21 × 31 × 51 × 111 × 971 × 160071
LCM(32010,32014) = 512384070
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