Least Common Multiple of 412 and 414

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 414 the smallest integer that is 85284 that is divisible by both numbers.

Least Common Multiple (LCM) of 412 and 414 is 85284.

LCM(412,414) = 85284

LCM of 412 and 414

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

LCM of:
and

Least Common Multiple of 412 and 414

LCM of 412 and 414 is 85284

Least common multiple can be found by multiplying the highest exponent prime factors of 412 and 414. First we will calculate the prime factors of 412 and 414.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 412 and 414.

LCM(412,414) = 22×32×231×1031
LCM(412,414) = 85284

Factors of 412

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

1, 2, 4, 103, 206, 412

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

Least Common Multiple of 412 and 414 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 414, than apply into the LCM equation.

GCF(412,414) = 2
LCM(412,414) = ( 412 × 414) / 2
LCM(412,414) = 170568 / 2
LCM(412,414) = 85284

Properties of LCM 412 and 414

(i) The LCM of 414 and 412 is associative

LCM of 412 and 414 = LCM of 414 and 412

Related Least Common Multiples of 412

Related Least Common Multiples of 414

Frequently Asked Questions on LCM of 412 and 414

1. What is the LCM of 412 and 414?

Answer: LCM of 412 and 414 is 85284.

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 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.

4. How to Find the LCM of 412 and 414?

Answer:

Least Common Multiple of 412 and 414 = 85284

Step 1: Find the prime factorization of 412

412 = 2 x 2 x 103

Step 2: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

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

LCM = 85284 = 2 x 2 x 3 x 3 x 23 x 103

Step 4: Therefore, the least common multiple of 412 and 414 is 85284.