Least Common Multiple of 40 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 40 and 49 the smallest integer that is 1960 that is divisible by both numbers.

Least Common Multiple (LCM) of 40 and 49 is 1960.

LCM(40,49) = 1960

LCM of 40 and 49

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

LCM of:
and

Least Common Multiple of 40 and 49

LCM of 40 and 49 is 1960

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 49. First we will calculate the prime factors of 40 and 49.

Prime Factorization of 40


2 40
2 20
2 10
5 5
1

Prime factors of 40 are 2,5. Prime factorization of 40 in exponential form is:

40 = 23×51

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 40 and 49.

LCM(40,49) = 23×51×72
LCM(40,49) = 1960

Factors of 40

List of positive integer factors of 40 that divides 40 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40

Factors of 49

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

1, 7, 49

Least Common Multiple of 40 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 40 and 49, than apply into the LCM equation.

GCF(40,49) = 1
LCM(40,49) = ( 40 × 49) / 1
LCM(40,49) = 1960 / 1
LCM(40,49) = 1960

Properties of LCM 40 and 49

(i) The LCM of 49 and 40 is associative

LCM of 40 and 49 = LCM of 49 and 40

Related Least Common Multiples of 40

Related Least Common Multiples of 49

Frequently Asked Questions on LCM of 40 and 49

1. What is the LCM of 40 and 49?

Answer: LCM of 40 and 49 is 1960.

2. What are the Factors of 40?

Answer: Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. There are 8 integers that are factors of 40. The greatest factor of 40 is 40.

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 40 and 49?

Answer:

Least Common Multiple of 40 and 49 = 1960

Step 1: Find the prime factorization of 40

40 = 2 x 2 x 2 x 5

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 = 1960 = 2 x 2 x 2 x 5 x 7 x 7

Step 4: Therefore, the least common multiple of 40 and 49 is 1960.