Least Common Multiple of 448 and 450

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 450 the smallest integer that is 100800 that is divisible by both numbers.

Least Common Multiple (LCM) of 448 and 450 is 100800.

LCM(448,450) = 100800

LCM of 448 and 450

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

LCM of:
and

Least Common Multiple of 448 and 450

LCM of 448 and 450 is 100800

Least common multiple can be found by multiplying the highest exponent prime factors of 448 and 450. First we will calculate the prime factors of 448 and 450.

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 450


2 450
3 225
3 75
5 25
5 5
1

Prime factors of 450 are 2, 3,5. Prime factorization of 450 in exponential form is:

450 = 21×32×52

Now multiplying the highest exponent prime factors to calculate the LCM of 448 and 450.

LCM(448,450) = 26×32×52×71
LCM(448,450) = 100800

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 450

List of positive integer factors of 450 that divides 450 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450

Least Common Multiple of 448 and 450 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 450, than apply into the LCM equation.

GCF(448,450) = 2
LCM(448,450) = ( 448 × 450) / 2
LCM(448,450) = 201600 / 2
LCM(448,450) = 100800

Properties of LCM 448 and 450

(i) The LCM of 450 and 448 is associative

LCM of 448 and 450 = LCM of 450 and 448

Related Least Common Multiples of 448

Related Least Common Multiples of 450

Frequently Asked Questions on LCM of 448 and 450

1. What is the LCM of 448 and 450?

Answer: LCM of 448 and 450 is 100800.

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 450?

Answer: Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450. There are 18 integers that are factors of 450. The greatest factor of 450 is 450.

4. How to Find the LCM of 448 and 450?

Answer:

Least Common Multiple of 448 and 450 = 100800

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 450

450 = 2 x 3 x 3 x 5 x 5

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

LCM = 100800 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7

Step 4: Therefore, the least common multiple of 448 and 450 is 100800.