Least Common Multiple of 407 and 408

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 407 and 408 the smallest integer that is 166056 that is divisible by both numbers.

Least Common Multiple (LCM) of 407 and 408 is 166056.

LCM(407,408) = 166056

LCM of 407 and 408

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

LCM of:
and

Least Common Multiple of 407 and 408

LCM of 407 and 408 is 166056

Least common multiple can be found by multiplying the highest exponent prime factors of 407 and 408. First we will calculate the prime factors of 407 and 408.

Prime Factorization of 407


11 407
37 37
1

Prime factors of 407 are 11,37. Prime factorization of 407 in exponential form is:

407 = 111×371

Prime Factorization of 408


2 408
2 204
2 102
3 51
17 17
1

Prime factors of 408 are 2, 3,17. Prime factorization of 408 in exponential form is:

408 = 23×31×171

Now multiplying the highest exponent prime factors to calculate the LCM of 407 and 408.

LCM(407,408) = 23×31×111×171×371
LCM(407,408) = 166056

Factors of 407

List of positive integer factors of 407 that divides 407 without a remainder.

1, 11, 37, 407

Factors of 408

List of positive integer factors of 408 that divides 408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

Least Common Multiple of 407 and 408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 407 and 408, than apply into the LCM equation.

GCF(407,408) = 1
LCM(407,408) = ( 407 × 408) / 1
LCM(407,408) = 166056 / 1
LCM(407,408) = 166056

Properties of LCM 407 and 408

(i) The LCM of 408 and 407 is associative

LCM of 407 and 408 = LCM of 408 and 407

Related Least Common Multiples of 407

Related Least Common Multiples of 408

Frequently Asked Questions on LCM of 407 and 408

1. What is the LCM of 407 and 408?

Answer: LCM of 407 and 408 is 166056.

2. What are the Factors of 407?

Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.

3. What are the Factors of 408?

Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.

4. How to Find the LCM of 407 and 408?

Answer:

Least Common Multiple of 407 and 408 = 166056

Step 1: Find the prime factorization of 407

407 = 11 x 37

Step 2: Find the prime factorization of 408

408 = 2 x 2 x 2 x 3 x 17

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

LCM = 166056 = 2 x 2 x 2 x 3 x 11 x 17 x 37

Step 4: Therefore, the least common multiple of 407 and 408 is 166056.