Least Common Multiple of 412 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 412 and 420 the smallest integer that is 43260 that is divisible by both numbers.

Least Common Multiple (LCM) of 412 and 420 is 43260.

LCM(412,420) = 43260

LCM of 412 and 420

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

LCM of:
and

Least Common Multiple of 412 and 420

LCM of 412 and 420 is 43260

Least common multiple can be found by multiplying the highest exponent prime factors of 412 and 420. First we will calculate the prime factors of 412 and 420.

Prime Factorization of 412


2 412
2 206
103 103
1

Prime factors of 412 are 2,103. Prime factorization of 412 in exponential form is:

412 = 22×1031

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 412 and 420.

LCM(412,420) = 22×31×51×71×1031
LCM(412,420) = 43260

Factors of 412

List of positive integer factors of 412 that divides 412 without a remainder.

1, 2, 4, 103, 206, 412

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 412 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 412 and 420, than apply into the LCM equation.

GCF(412,420) = 4
LCM(412,420) = ( 412 × 420) / 4
LCM(412,420) = 173040 / 4
LCM(412,420) = 43260

Properties of LCM 412 and 420

(i) The LCM of 420 and 412 is associative

LCM of 412 and 420 = LCM of 420 and 412

Related Least Common Multiples of 412

Related Least Common Multiples of 420

Frequently Asked Questions on LCM of 412 and 420

1. What is the LCM of 412 and 420?

Answer: LCM of 412 and 420 is 43260.

2. What are the Factors of 412?

Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.

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 412 and 420?

Answer:

Least Common Multiple of 412 and 420 = 43260

Step 1: Find the prime factorization of 412

412 = 2 x 2 x 103

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 = 43260 = 2 x 2 x 3 x 5 x 7 x 103

Step 4: Therefore, the least common multiple of 412 and 420 is 43260.