Least Common Multiple of 402 and 407

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 407 the smallest integer that is 163614 that is divisible by both numbers.

Least Common Multiple (LCM) of 402 and 407 is 163614.

LCM(402,407) = 163614

LCM of 402 and 407

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

LCM of:
and

Least Common Multiple of 402 and 407

LCM of 402 and 407 is 163614

Least common multiple can be found by multiplying the highest exponent prime factors of 402 and 407. First we will calculate the prime factors of 402 and 407.

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 407


11 407
37 37
1

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

407 = 111×371

Now multiplying the highest exponent prime factors to calculate the LCM of 402 and 407.

LCM(402,407) = 21×31×111×371×671
LCM(402,407) = 163614

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 407

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

1, 11, 37, 407

Least Common Multiple of 402 and 407 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 407, than apply into the LCM equation.

GCF(402,407) = 1
LCM(402,407) = ( 402 × 407) / 1
LCM(402,407) = 163614 / 1
LCM(402,407) = 163614

Properties of LCM 402 and 407

(i) The LCM of 407 and 402 is associative

LCM of 402 and 407 = LCM of 407 and 402

Related Least Common Multiples of 402

Related Least Common Multiples of 407

Frequently Asked Questions on LCM of 402 and 407

1. What is the LCM of 402 and 407?

Answer: LCM of 402 and 407 is 163614.

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 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.

4. How to Find the LCM of 402 and 407?

Answer:

Least Common Multiple of 402 and 407 = 163614

Step 1: Find the prime factorization of 402

402 = 2 x 3 x 67

Step 2: Find the prime factorization of 407

407 = 11 x 37

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

LCM = 163614 = 2 x 3 x 11 x 37 x 67

Step 4: Therefore, the least common multiple of 402 and 407 is 163614.