Least Common Multiple of 1408 and 1416

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1408 and 1416 the smallest integer that is 249216 that is divisible by both numbers.

Least Common Multiple (LCM) of 1408 and 1416 is 249216.

LCM(1408,1416) = 249216

LCM of 1408 and 1416

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

LCM of:
and

Least Common Multiple of 1408 and 1416

LCM of 1408 and 1416 is 249216

Least common multiple can be found by multiplying the highest exponent prime factors of 1408 and 1416. First we will calculate the prime factors of 1408 and 1416.

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

Prime Factorization of 1416


2 1416
2 708
2 354
3 177
59 59
1

Prime factors of 1416 are 2, 3,59. Prime factorization of 1416 in exponential form is:

1416 = 23×31×591

Now multiplying the highest exponent prime factors to calculate the LCM of 1408 and 1416.

LCM(1408,1416) = 27×31×111×591
LCM(1408,1416) = 249216

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

Factors of 1416

List of positive integer factors of 1416 that divides 1416 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416

Least Common Multiple of 1408 and 1416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1408 and 1416, than apply into the LCM equation.

GCF(1408,1416) = 8
LCM(1408,1416) = ( 1408 × 1416) / 8
LCM(1408,1416) = 1993728 / 8
LCM(1408,1416) = 249216

Properties of LCM 1408 and 1416

(i) The LCM of 1416 and 1408 is associative

LCM of 1408 and 1416 = LCM of 1416 and 1408

Related Least Common Multiples of 1408

Related Least Common Multiples of 1416

Frequently Asked Questions on LCM of 1408 and 1416

1. What is the LCM of 1408 and 1416?

Answer: LCM of 1408 and 1416 is 249216.

2. 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.

3. What are the Factors of 1416?

Answer: Factors of 1416 are 1, 2, 3, 4, 6, 8, 12, 24, 59, 118, 177, 236, 354, 472, 708, 1416. There are 16 integers that are factors of 1416. The greatest factor of 1416 is 1416.

4. How to Find the LCM of 1408 and 1416?

Answer:

Least Common Multiple of 1408 and 1416 = 249216

Step 1: Find the prime factorization of 1408

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

Step 2: Find the prime factorization of 1416

1416 = 2 x 2 x 2 x 3 x 59

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

LCM = 249216 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11 x 59

Step 4: Therefore, the least common multiple of 1408 and 1416 is 249216.