Least Common Multiple of 414 and 415

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 415 the smallest integer that is 171810 that is divisible by both numbers.

Least Common Multiple (LCM) of 414 and 415 is 171810.

LCM(414,415) = 171810

LCM of 414 and 415

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

LCM of:
and

Least Common Multiple of 414 and 415

LCM of 414 and 415 is 171810

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 415. First we will calculate the prime factors of 414 and 415.

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 415


5 415
83 83
1

Prime factors of 415 are 5,83. Prime factorization of 415 in exponential form is:

415 = 51×831

Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 415.

LCM(414,415) = 21×32×51×231×831
LCM(414,415) = 171810

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 415

List of positive integer factors of 415 that divides 415 without a remainder.

1, 5, 83, 415

Least Common Multiple of 414 and 415 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 415, than apply into the LCM equation.

GCF(414,415) = 1
LCM(414,415) = ( 414 × 415) / 1
LCM(414,415) = 171810 / 1
LCM(414,415) = 171810

Properties of LCM 414 and 415

(i) The LCM of 415 and 414 is associative

LCM of 414 and 415 = LCM of 415 and 414

Related Least Common Multiples of 414

Related Least Common Multiples of 415

Frequently Asked Questions on LCM of 414 and 415

1. What is the LCM of 414 and 415?

Answer: LCM of 414 and 415 is 171810.

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 415?

Answer: Factors of 415 are 1, 5, 83, 415. There are 4 integers that are factors of 415. The greatest factor of 415 is 415.

4. How to Find the LCM of 414 and 415?

Answer:

Least Common Multiple of 414 and 415 = 171810

Step 1: Find the prime factorization of 414

414 = 2 x 3 x 3 x 23

Step 2: Find the prime factorization of 415

415 = 5 x 83

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

LCM = 171810 = 2 x 3 x 3 x 5 x 23 x 83

Step 4: Therefore, the least common multiple of 414 and 415 is 171810.