What is the Least Common Multiple of 196 and 210?
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 196 and 210 is 2940.
LCM(196,210) = 2940
Least Common Multiple of 196 and 210 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 196 and 210, than apply into the LCM equation.
GCF(196,210) = 14
LCM(196,210) = ( 196 × 210) / 14
LCM(196,210) = 41160 / 14
LCM(196,210) = 2940
Least Common Multiple (LCM) of 196 and 210 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 196 and 210. First we will calculate the prime factors of 196 and 210.
Prime Factorization of 196
Prime factors of 196 are 2, 7. Prime factorization of 196 in exponential form is:
196 = 22 × 72
Prime Factorization of 210
Prime factors of 210 are 2, 3, 5, 7. Prime factorization of 210 in exponential form is:
210 = 21 × 31 × 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 196 and 210.
LCM(196,210) = 22 × 72 × 31 × 51
LCM(196,210) = 2940
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