What is the Least Common Multiple of 196 and 214?
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 214 is 20972.
LCM(196,214) = 20972
Least Common Multiple of 196 and 214 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 214, than apply into the LCM equation.
GCF(196,214) = 2
LCM(196,214) = ( 196 × 214) / 2
LCM(196,214) = 41944 / 2
LCM(196,214) = 20972
Least Common Multiple (LCM) of 196 and 214 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 196 and 214. First we will calculate the prime factors of 196 and 214.
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 214
Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:
214 = 21 × 1071
Now multiplying the highest exponent prime factors to calculate the LCM of 196 and 214.
LCM(196,214) = 22 × 72 × 1071
LCM(196,214) = 20972
Related Least Common Multiples of 196
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Related Least Common Multiples of 214
- LCM of 214 and 218
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- LCM of 214 and 221
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- LCM of 214 and 223
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