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 57 the smallest integer that is 2280 that is divisible by both numbers.
Least Common Multiple (LCM) of 40 and 57 is 2280.
LCM(40,57) = 2280
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 57. First we will calculate the prime factors of 40 and 57.
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 57
3 | 57 |
19 | 19 |
1 |
Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:
57 = 31×191
Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 57.
LCM(40,57) = 23×31×51×191
LCM(40,57) = 2280
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 57
List of positive integer factors of 57 that divides 57 without a remainder.
1, 3, 19, 57
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 57, than apply into the LCM equation.
GCF(40,57) = 1
LCM(40,57) = ( 40 × 57) / 1
LCM(40,57) = 2280 / 1
LCM(40,57) = 2280
(i) The LCM of 57 and 40 is associative
LCM of 40 and 57 = LCM of 57 and 40
1. What is the LCM of 40 and 57?
Answer: LCM of 40 and 57 is 2280.
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 57?
Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.
4. How to Find the LCM of 40 and 57?
Answer:
Least Common Multiple of 40 and 57 = 2280
Step 1: Find the prime factorization of 40
40 = 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 57
57 = 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 = 2280 = 2 x 2 x 2 x 3 x 5 x 19
Step 4: Therefore, the least common multiple of 40 and 57 is 2280.