Least Common Multiple of 1403 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 1403 and 1408 the smallest integer that is 1975424 that is divisible by both numbers.

Least Common Multiple (LCM) of 1403 and 1408 is 1975424.

LCM(1403,1408) = 1975424

LCM of 1403 and 1408

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

LCM of:
and

Least Common Multiple of 1403 and 1408

LCM of 1403 and 1408 is 1975424

Least common multiple can be found by multiplying the highest exponent prime factors of 1403 and 1408. First we will calculate the prime factors of 1403 and 1408.

Prime Factorization of 1403


23 1403
61 61
1

Prime factors of 1403 are 23,61. Prime factorization of 1403 in exponential form is:

1403 = 231×611

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 1403 and 1408.

LCM(1403,1408) = 27×111×231×611
LCM(1403,1408) = 1975424

Factors of 1403

List of positive integer factors of 1403 that divides 1403 without a remainder.

1, 23, 61, 1403

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 1403 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 1403 and 1408, than apply into the LCM equation.

GCF(1403,1408) = 1
LCM(1403,1408) = ( 1403 × 1408) / 1
LCM(1403,1408) = 1975424 / 1
LCM(1403,1408) = 1975424

Properties of LCM 1403 and 1408

(i) The LCM of 1408 and 1403 is associative

LCM of 1403 and 1408 = LCM of 1408 and 1403

Related Least Common Multiples of 1403

Related Least Common Multiples of 1408

Frequently Asked Questions on LCM of 1403 and 1408

1. What is the LCM of 1403 and 1408?

Answer: LCM of 1403 and 1408 is 1975424.

2. What are the Factors of 1403?

Answer: Factors of 1403 are 1, 23, 61, 1403. There are 4 integers that are factors of 1403. The greatest factor of 1403 is 1403.

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 1403 and 1408?

Answer:

Least Common Multiple of 1403 and 1408 = 1975424

Step 1: Find the prime factorization of 1403

1403 = 23 x 61

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 = 1975424 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 23 x 61

Step 4: Therefore, the least common multiple of 1403 and 1408 is 1975424.