Least Common Multiple of 418 and 420

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 420 the smallest integer that is 87780 that is divisible by both numbers.

Least Common Multiple (LCM) of 418 and 420 is 87780.

LCM(418,420) = 87780

LCM of 418 and 420

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 418 and 420

LCM of 418 and 420 is 87780

Least common multiple can be found by multiplying the highest exponent prime factors of 418 and 420. First we will calculate the prime factors of 418 and 420.

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 420


2 420
2 210
3 105
5 35
7 7
1

Prime factors of 420 are 2, 3, 5,7. Prime factorization of 420 in exponential form is:

420 = 22×31×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 418 and 420.

LCM(418,420) = 22×31×51×71×111×191
LCM(418,420) = 87780

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 420

List of positive integer factors of 420 that divides 420 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

Least Common Multiple of 418 and 420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 418 and 420, than apply into the LCM equation.

GCF(418,420) = 2
LCM(418,420) = ( 418 × 420) / 2
LCM(418,420) = 175560 / 2
LCM(418,420) = 87780

Properties of LCM 418 and 420

(i) The LCM of 420 and 418 is associative

LCM of 418 and 420 = LCM of 420 and 418

Related Least Common Multiples of 418

Related Least Common Multiples of 420

Frequently Asked Questions on LCM of 418 and 420

1. What is the LCM of 418 and 420?

Answer: LCM of 418 and 420 is 87780.

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 420?

Answer: Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420. There are 24 integers that are factors of 420. The greatest factor of 420 is 420.

4. How to Find the LCM of 418 and 420?

Answer:

Least Common Multiple of 418 and 420 = 87780

Step 1: Find the prime factorization of 418

418 = 2 x 11 x 19

Step 2: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 87780 = 2 x 2 x 3 x 5 x 7 x 11 x 19

Step 4: Therefore, the least common multiple of 418 and 420 is 87780.