What is the Least Common Multiple of 975 and 980?
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 975 and 980 is 191100.
LCM(975,980) = 191100
Least Common Multiple of 975 and 980 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 975 and 980, than apply into the LCM equation.
GCF(975,980) = 5
LCM(975,980) = ( 975 × 980) / 5
LCM(975,980) = 955500 / 5
LCM(975,980) = 191100
Least Common Multiple (LCM) of 975 and 980 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 975 and 980. First we will calculate the prime factors of 975 and 980.
Prime Factorization of 975
Prime factors of 975 are 3, 5, 13. Prime factorization of 975 in exponential form is:
975 = 31 × 52 × 131
Prime Factorization of 980
Prime factors of 980 are 2, 5, 7. Prime factorization of 980 in exponential form is:
980 = 22 × 51 × 72
Now multiplying the highest exponent prime factors to calculate the LCM of 975 and 980.
LCM(975,980) = 31 × 52 × 131 × 22 × 72
LCM(975,980) = 191100
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