Least Common Multiple of 448 and 456

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 448 and 456 the smallest integer that is 25536 that is divisible by both numbers.

Least Common Multiple (LCM) of 448 and 456 is 25536.

LCM(448,456) = 25536

LCM of 448 and 456

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

LCM of:
and

Least Common Multiple of 448 and 456

LCM of 448 and 456 is 25536

Least common multiple can be found by multiplying the highest exponent prime factors of 448 and 456. First we will calculate the prime factors of 448 and 456.

Prime Factorization of 448


2 448
2 224
2 112
2 56
2 28
2 14
7 7
1

Prime factors of 448 are 2,7. Prime factorization of 448 in exponential form is:

448 = 26×71

Prime Factorization of 456


2 456
2 228
2 114
3 57
19 19
1

Prime factors of 456 are 2, 3,19. Prime factorization of 456 in exponential form is:

456 = 23×31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 448 and 456.

LCM(448,456) = 26×31×71×191
LCM(448,456) = 25536

Factors of 448

List of positive integer factors of 448 that divides 448 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448

Factors of 456

List of positive integer factors of 456 that divides 456 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456

Least Common Multiple of 448 and 456 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 448 and 456, than apply into the LCM equation.

GCF(448,456) = 8
LCM(448,456) = ( 448 × 456) / 8
LCM(448,456) = 204288 / 8
LCM(448,456) = 25536

Properties of LCM 448 and 456

(i) The LCM of 456 and 448 is associative

LCM of 448 and 456 = LCM of 456 and 448

Related Least Common Multiples of 448

Related Least Common Multiples of 456

Frequently Asked Questions on LCM of 448 and 456

1. What is the LCM of 448 and 456?

Answer: LCM of 448 and 456 is 25536.

2. What are the Factors of 448?

Answer: Factors of 448 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448. There are 14 integers that are factors of 448. The greatest factor of 448 is 448.

3. What are the Factors of 456?

Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.

4. How to Find the LCM of 448 and 456?

Answer:

Least Common Multiple of 448 and 456 = 25536

Step 1: Find the prime factorization of 448

448 = 2 x 2 x 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 456

456 = 2 x 2 x 2 x 3 x 19

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

LCM = 25536 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 448 and 456 is 25536.