Least Common Multiple of 414 and 416

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 416 the smallest integer that is 86112 that is divisible by both numbers.

Least Common Multiple (LCM) of 414 and 416 is 86112.

LCM(414,416) = 86112

LCM of 414 and 416

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

LCM of:
and

Least Common Multiple of 414 and 416

LCM of 414 and 416 is 86112

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 416. First we will calculate the prime factors of 414 and 416.

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 416


2 416
2 208
2 104
2 52
2 26
13 13
1

Prime factors of 416 are 2,13. Prime factorization of 416 in exponential form is:

416 = 25×131

Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 416.

LCM(414,416) = 25×32×131×231
LCM(414,416) = 86112

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 416

List of positive integer factors of 416 that divides 416 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416

Least Common Multiple of 414 and 416 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 416, than apply into the LCM equation.

GCF(414,416) = 2
LCM(414,416) = ( 414 × 416) / 2
LCM(414,416) = 172224 / 2
LCM(414,416) = 86112

Properties of LCM 414 and 416

(i) The LCM of 416 and 414 is associative

LCM of 414 and 416 = LCM of 416 and 414

Related Least Common Multiples of 414

Related Least Common Multiples of 416

Frequently Asked Questions on LCM of 414 and 416

1. What is the LCM of 414 and 416?

Answer: LCM of 414 and 416 is 86112.

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 416?

Answer: Factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416. There are 12 integers that are factors of 416. The greatest factor of 416 is 416.

4. How to Find the LCM of 414 and 416?

Answer:

Least Common Multiple of 414 and 416 = 86112

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 416

416 = 2 x 2 x 2 x 2 x 2 x 13

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

LCM = 86112 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 13 x 23

Step 4: Therefore, the least common multiple of 414 and 416 is 86112.