Least Common Multiple of 420 and 426

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 420 and 426 the smallest integer that is 29820 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 426 is 29820.

LCM(420,426) = 29820

LCM of 420 and 426

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

LCM of:
and

Least Common Multiple of 420 and 426

LCM of 420 and 426 is 29820

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 426. First we will calculate the prime factors of 420 and 426.

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

Prime Factorization of 426


2 426
3 213
71 71
1

Prime factors of 426 are 2, 3,71. Prime factorization of 426 in exponential form is:

426 = 21×31×711

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 426.

LCM(420,426) = 22×31×51×71×711
LCM(420,426) = 29820

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

Factors of 426

List of positive integer factors of 426 that divides 426 without a remainder.

1, 2, 3, 6, 71, 142, 213, 426

Least Common Multiple of 420 and 426 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 426, than apply into the LCM equation.

GCF(420,426) = 6
LCM(420,426) = ( 420 × 426) / 6
LCM(420,426) = 178920 / 6
LCM(420,426) = 29820

Properties of LCM 420 and 426

(i) The LCM of 426 and 420 is associative

LCM of 420 and 426 = LCM of 426 and 420

Related Least Common Multiples of 420

Related Least Common Multiples of 426

Frequently Asked Questions on LCM of 420 and 426

1. What is the LCM of 420 and 426?

Answer: LCM of 420 and 426 is 29820.

2. 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.

3. What are the Factors of 426?

Answer: Factors of 426 are 1, 2, 3, 6, 71, 142, 213, 426. There are 8 integers that are factors of 426. The greatest factor of 426 is 426.

4. How to Find the LCM of 420 and 426?

Answer:

Least Common Multiple of 420 and 426 = 29820

Step 1: Find the prime factorization of 420

420 = 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 426

426 = 2 x 3 x 71

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

LCM = 29820 = 2 x 2 x 3 x 5 x 7 x 71

Step 4: Therefore, the least common multiple of 420 and 426 is 29820.