Least Common Multiple of 420 and 422

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 422 the smallest integer that is 88620 that is divisible by both numbers.

Least Common Multiple (LCM) of 420 and 422 is 88620.

LCM(420,422) = 88620

LCM of 420 and 422

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

LCM of:
and

Least Common Multiple of 420 and 422

LCM of 420 and 422 is 88620

Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 422. First we will calculate the prime factors of 420 and 422.

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 422


2 422
211 211
1

Prime factors of 422 are 2,211. Prime factorization of 422 in exponential form is:

422 = 21×2111

Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 422.

LCM(420,422) = 22×31×51×71×2111
LCM(420,422) = 88620

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 422

List of positive integer factors of 422 that divides 422 without a remainder.

1, 2, 211, 422

Least Common Multiple of 420 and 422 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 422, than apply into the LCM equation.

GCF(420,422) = 2
LCM(420,422) = ( 420 × 422) / 2
LCM(420,422) = 177240 / 2
LCM(420,422) = 88620

Properties of LCM 420 and 422

(i) The LCM of 422 and 420 is associative

LCM of 420 and 422 = LCM of 422 and 420

Frequently Asked Questions on LCM of 420 and 422

1. What is the LCM of 420 and 422?

Answer: LCM of 420 and 422 is 88620.

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 422?

Answer: Factors of 422 are 1, 2, 211, 422. There are 4 integers that are factors of 422. The greatest factor of 422 is 422.

4. How to Find the LCM of 420 and 422?

Answer:

Least Common Multiple of 420 and 422 = 88620

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 422

422 = 2 x 211

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

LCM = 88620 = 2 x 2 x 3 x 5 x 7 x 211

Step 4: Therefore, the least common multiple of 420 and 422 is 88620.