What is the Least Common Multiple of 8730 and 8740?
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 8730 and 8740 is 7630020.
LCM(8730,8740) = 7630020
Least Common Multiple of 8730 and 8740 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8730 and 8740, than apply into the LCM equation.
GCF(8730,8740) = 10
LCM(8730,8740) = ( 8730 × 8740) / 10
LCM(8730,8740) = 76300200 / 10
LCM(8730,8740) = 7630020
Least Common Multiple (LCM) of 8730 and 8740 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 8730 and 8740. First we will calculate the prime factors of 8730 and 8740.
Prime Factorization of 8730
Prime factors of 8730 are 2, 3, 5, 97. Prime factorization of 8730 in exponential form is:
8730 = 21 × 32 × 51 × 971
Prime Factorization of 8740
Prime factors of 8740 are 2, 5, 19, 23. Prime factorization of 8740 in exponential form is:
8740 = 22 × 51 × 191 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 8730 and 8740.
LCM(8730,8740) = 22 × 32 × 51 × 971 × 191 × 231
LCM(8730,8740) = 7630020
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