Least Common Multiple of 48 and 49

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 49 the smallest integer that is 2352 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 49 is 2352.

LCM(48,49) = 2352

LCM of 48 and 49

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

LCM of:
and

Least Common Multiple of 48 and 49

LCM of 48 and 49 is 2352

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 49. First we will calculate the prime factors of 48 and 49.

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 49


7 49
7 7
1

Prime factors of 49 are 7. Prime factorization of 49 in exponential form is:

49 = 72

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 49.

LCM(48,49) = 24×31×72
LCM(48,49) = 2352

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 49

List of positive integer factors of 49 that divides 49 without a remainder.

1, 7, 49

Least Common Multiple of 48 and 49 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 49, than apply into the LCM equation.

GCF(48,49) = 1
LCM(48,49) = ( 48 × 49) / 1
LCM(48,49) = 2352 / 1
LCM(48,49) = 2352

Properties of LCM 48 and 49

(i) The LCM of 49 and 48 is associative

LCM of 48 and 49 = LCM of 49 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 49

Frequently Asked Questions on LCM of 48 and 49

1. What is the LCM of 48 and 49?

Answer: LCM of 48 and 49 is 2352.

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 49?

Answer: Factors of 49 are 1, 7, 49. There are 3 integers that are factors of 49. The greatest factor of 49 is 49.

4. How to Find the LCM of 48 and 49?

Answer:

Least Common Multiple of 48 and 49 = 2352

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 49

49 = 7 x 7

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

LCM = 2352 = 2 x 2 x 2 x 2 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 48 and 49 is 2352.