Least Common Multiple of 48 and 50

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 48 and 50 the smallest integer that is 1200 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 50 is 1200.

LCM(48,50) = 1200

LCM of 48 and 50

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

LCM of:
and

Least Common Multiple of 48 and 50

LCM of 48 and 50 is 1200

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 50. First we will calculate the prime factors of 48 and 50.

Prime Factorization of 48


2 48
2 24
2 12
2 6
3 3
1

Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:

48 = 24×31

Prime Factorization of 50


2 50
5 25
5 5
1

Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is:

50 = 21×52

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 50.

LCM(48,50) = 24×31×52
LCM(48,50) = 1200

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 50

List of positive integer factors of 50 that divides 50 without a remainder.

1, 2, 5, 10, 25, 50

Least Common Multiple of 48 and 50 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 50, than apply into the LCM equation.

GCF(48,50) = 2
LCM(48,50) = ( 48 × 50) / 2
LCM(48,50) = 2400 / 2
LCM(48,50) = 1200

Properties of LCM 48 and 50

(i) The LCM of 50 and 48 is associative

LCM of 48 and 50 = LCM of 50 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 50

Frequently Asked Questions on LCM of 48 and 50

1. What is the LCM of 48 and 50?

Answer: LCM of 48 and 50 is 1200.

2. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

3. What are the Factors of 50?

Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50.

4. How to Find the LCM of 48 and 50?

Answer:

Least Common Multiple of 48 and 50 = 1200

Step 1: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 50

50 = 2 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 = 1200 = 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 48 and 50 is 1200.