Least Common Multiple of 414 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 414 and 420 the smallest integer that is 28980 that is divisible by both numbers.

Least Common Multiple (LCM) of 414 and 420 is 28980.

LCM(414,420) = 28980

LCM of 414 and 420

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

LCM of:
and

Least Common Multiple of 414 and 420

LCM of 414 and 420 is 28980

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 420. First we will calculate the prime factors of 414 and 420.

Prime Factorization of 414


2 414
3 207
3 69
23 23
1

Prime factors of 414 are 2, 3,23. Prime factorization of 414 in exponential form is:

414 = 21×32×231

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 414 and 420.

LCM(414,420) = 22×32×51×71×231
LCM(414,420) = 28980

Factors of 414

List of positive integer factors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

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 414 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 414 and 420, than apply into the LCM equation.

GCF(414,420) = 6
LCM(414,420) = ( 414 × 420) / 6
LCM(414,420) = 173880 / 6
LCM(414,420) = 28980

Properties of LCM 414 and 420

(i) The LCM of 420 and 414 is associative

LCM of 414 and 420 = LCM of 420 and 414

Related Least Common Multiples of 414

Related Least Common Multiples of 420

Frequently Asked Questions on LCM of 414 and 420

1. What is the LCM of 414 and 420?

Answer: LCM of 414 and 420 is 28980.

2. What are the Factors of 414?

Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.

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 414 and 420?

Answer:

Least Common Multiple of 414 and 420 = 28980

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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 = 28980 = 2 x 2 x 3 x 3 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 414 and 420 is 28980.