Least Common Multiple of 414 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 414 and 422 the smallest integer that is 87354 that is divisible by both numbers.

Least Common Multiple (LCM) of 414 and 422 is 87354.

LCM(414,422) = 87354

LCM of 414 and 422

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

LCM of:
and

Least Common Multiple of 414 and 422

LCM of 414 and 422 is 87354

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 422. First we will calculate the prime factors of 414 and 422.

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 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 414 and 422.

LCM(414,422) = 21×32×231×2111
LCM(414,422) = 87354

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 422

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

1, 2, 211, 422

Least Common Multiple of 414 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 414 and 422, than apply into the LCM equation.

GCF(414,422) = 2
LCM(414,422) = ( 414 × 422) / 2
LCM(414,422) = 174708 / 2
LCM(414,422) = 87354

Properties of LCM 414 and 422

(i) The LCM of 422 and 414 is associative

LCM of 414 and 422 = LCM of 422 and 414

Related Least Common Multiples of 414

Related Least Common Multiples of 422

Frequently Asked Questions on LCM of 414 and 422

1. What is the LCM of 414 and 422?

Answer: LCM of 414 and 422 is 87354.

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 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 414 and 422?

Answer:

Least Common Multiple of 414 and 422 = 87354

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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 = 87354 = 2 x 3 x 3 x 23 x 211

Step 4: Therefore, the least common multiple of 414 and 422 is 87354.