Least Common Multiple of 402 and 409

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 402 and 409 the smallest integer that is 164418 that is divisible by both numbers.

Least Common Multiple (LCM) of 402 and 409 is 164418.

LCM(402,409) = 164418

LCM of 402 and 409

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

LCM of:
and

Least Common Multiple of 402 and 409

LCM of 402 and 409 is 164418

Least common multiple can be found by multiplying the highest exponent prime factors of 402 and 409. First we will calculate the prime factors of 402 and 409.

Prime Factorization of 402


2 402
3 201
67 67
1

Prime factors of 402 are 2, 3,67. Prime factorization of 402 in exponential form is:

402 = 21×31×671

Prime Factorization of 409


409 409
1

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 4091

Now multiplying the highest exponent prime factors to calculate the LCM of 402 and 409.

LCM(402,409) = 21×31×671×4091
LCM(402,409) = 164418

Factors of 402

List of positive integer factors of 402 that divides 402 without a remainder.

1, 2, 3, 6, 67, 134, 201, 402

Factors of 409

List of positive integer factors of 409 that divides 409 without a remainder.

1, 409

Least Common Multiple of 402 and 409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 402 and 409, than apply into the LCM equation.

GCF(402,409) = 1
LCM(402,409) = ( 402 × 409) / 1
LCM(402,409) = 164418 / 1
LCM(402,409) = 164418

Properties of LCM 402 and 409

(i) The LCM of 409 and 402 is associative

LCM of 402 and 409 = LCM of 409 and 402

Related Least Common Multiples of 402

Related Least Common Multiples of 409

Frequently Asked Questions on LCM of 402 and 409

1. What is the LCM of 402 and 409?

Answer: LCM of 402 and 409 is 164418.

2. What are the Factors of 402?

Answer: Factors of 402 are 1, 2, 3, 6, 67, 134, 201, 402. There are 8 integers that are factors of 402. The greatest factor of 402 is 402.

3. What are the Factors of 409?

Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.

4. How to Find the LCM of 402 and 409?

Answer:

Least Common Multiple of 402 and 409 = 164418

Step 1: Find the prime factorization of 402

402 = 2 x 3 x 67

Step 2: Find the prime factorization of 409

409 = 409

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

LCM = 164418 = 2 x 3 x 67 x 409

Step 4: Therefore, the least common multiple of 402 and 409 is 164418.