Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 418 and 421 the smallest integer that is 175978 that is divisible by both numbers.
Least Common Multiple (LCM) of 418 and 421 is 175978.
LCM(418,421) = 175978
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 418 and 421. First we will calculate the prime factors of 418 and 421.
Prime Factorization of 418
2 | 418 |
11 | 209 |
19 | 19 |
1 |
Prime factors of 418 are 2, 11,19. Prime factorization of 418 in exponential form is:
418 = 21×111×191
Prime Factorization of 421
421 | 421 |
1 |
Prime factors of 421 are 421. Prime factorization of 421 in exponential form is:
421 = 4211
Now multiplying the highest exponent prime factors to calculate the LCM of 418 and 421.
LCM(418,421) = 21×111×191×4211
LCM(418,421) = 175978
Factors of 418
List of positive integer factors of 418 that divides 418 without a remainder.
1, 2, 11, 19, 22, 38, 209, 418
Factors of 421
List of positive integer factors of 421 that divides 421 without a remainder.
1, 421
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 418 and 421, than apply into the LCM equation.
GCF(418,421) = 1
LCM(418,421) = ( 418 × 421) / 1
LCM(418,421) = 175978 / 1
LCM(418,421) = 175978
(i) The LCM of 421 and 418 is associative
LCM of 418 and 421 = LCM of 421 and 418
1. What is the LCM of 418 and 421?
Answer: LCM of 418 and 421 is 175978.
2. What are the Factors of 418?
Answer: Factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418. There are 8 integers that are factors of 418. The greatest factor of 418 is 418.
3. What are the Factors of 421?
Answer: Factors of 421 are 1, 421. There are 2 integers that are factors of 421. The greatest factor of 421 is 421.
4. How to Find the LCM of 418 and 421?
Answer:
Least Common Multiple of 418 and 421 = 175978
Step 1: Find the prime factorization of 418
418 = 2 x 11 x 19
Step 2: Find the prime factorization of 421
421 = 421
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 175978 = 2 x 11 x 19 x 421
Step 4: Therefore, the least common multiple of 418 and 421 is 175978.