Least Common Multiple of 1402 and 1408

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1402 and 1408 the smallest integer that is 987008 that is divisible by both numbers.

Least Common Multiple (LCM) of 1402 and 1408 is 987008.

LCM(1402,1408) = 987008

LCM of 1402 and 1408

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

LCM of:
and

Least Common Multiple of 1402 and 1408

LCM of 1402 and 1408 is 987008

Least common multiple can be found by multiplying the highest exponent prime factors of 1402 and 1408. First we will calculate the prime factors of 1402 and 1408.

Prime Factorization of 1402


2 1402
701 701
1

Prime factors of 1402 are 2,701. Prime factorization of 1402 in exponential form is:

1402 = 21×7011

Prime Factorization of 1408


2 1408
2 704
2 352
2 176
2 88
2 44
2 22
11 11
1

Prime factors of 1408 are 2,11. Prime factorization of 1408 in exponential form is:

1408 = 27×111

Now multiplying the highest exponent prime factors to calculate the LCM of 1402 and 1408.

LCM(1402,1408) = 27×111×7011
LCM(1402,1408) = 987008

Factors of 1402

List of positive integer factors of 1402 that divides 1402 without a remainder.

1, 2, 701, 1402

Factors of 1408

List of positive integer factors of 1408 that divides 1408 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408

Least Common Multiple of 1402 and 1408 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1402 and 1408, than apply into the LCM equation.

GCF(1402,1408) = 2
LCM(1402,1408) = ( 1402 × 1408) / 2
LCM(1402,1408) = 1974016 / 2
LCM(1402,1408) = 987008

Properties of LCM 1402 and 1408

(i) The LCM of 1408 and 1402 is associative

LCM of 1402 and 1408 = LCM of 1408 and 1402

Related Least Common Multiples of 1402

Related Least Common Multiples of 1408

Frequently Asked Questions on LCM of 1402 and 1408

1. What is the LCM of 1402 and 1408?

Answer: LCM of 1402 and 1408 is 987008.

2. What are the Factors of 1402?

Answer: Factors of 1402 are 1, 2, 701, 1402. There are 4 integers that are factors of 1402. The greatest factor of 1402 is 1402.

3. What are the Factors of 1408?

Answer: Factors of 1408 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704, 1408. There are 16 integers that are factors of 1408. The greatest factor of 1408 is 1408.

4. How to Find the LCM of 1402 and 1408?

Answer:

Least Common Multiple of 1402 and 1408 = 987008

Step 1: Find the prime factorization of 1402

1402 = 2 x 701

Step 2: Find the prime factorization of 1408

1408 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11

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

LCM = 987008 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 701

Step 4: Therefore, the least common multiple of 1402 and 1408 is 987008.