Least Common Multiple of 416 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 416 and 420 the smallest integer that is 43680 that is divisible by both numbers.

Least Common Multiple (LCM) of 416 and 420 is 43680.

LCM(416,420) = 43680

LCM of 416 and 420

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

LCM of:
and

Least Common Multiple of 416 and 420

LCM of 416 and 420 is 43680

Least common multiple can be found by multiplying the highest exponent prime factors of 416 and 420. First we will calculate the prime factors of 416 and 420.

Prime Factorization of 416


2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:

416 = 25×131

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 416 and 420.

LCM(416,420) = 25×31×51×71×131
LCM(416,420) = 43680

Factors of 416

List of positive integer factors of 416 that divides 416 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

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 416 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 416 and 420, than apply into the LCM equation.

GCF(416,420) = 4
LCM(416,420) = ( 416 × 420) / 4
LCM(416,420) = 174720 / 4
LCM(416,420) = 43680

Properties of LCM 416 and 420

(i) The LCM of 420 and 416 is associative

LCM of 416 and 420 = LCM of 420 and 416

Related Least Common Multiples of 416

Related Least Common Multiples of 420

Frequently Asked Questions on LCM of 416 and 420

1. What is the LCM of 416 and 420?

Answer: LCM of 416 and 420 is 43680.

2. What are the Factors of 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

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 416 and 420?

Answer:

Least Common Multiple of 416 and 420 = 43680

Step 1: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

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 = 43680 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 416 and 420 is 43680.