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 58 the smallest integer that is 1160 that is divisible by both numbers.
Least Common Multiple (LCM) of 40 and 58 is 1160.
LCM(40,58) = 1160
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 58. First we will calculate the prime factors of 40 and 58.
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 58
2 | 58 |
29 | 29 |
1 |
Prime factors of 58 are 2,29. Prime factorization of 58 in exponential form is:
58 = 21×291
Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 58.
LCM(40,58) = 23×51×291
LCM(40,58) = 1160
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 58
List of positive integer factors of 58 that divides 58 without a remainder.
1, 2, 29, 58
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 58, than apply into the LCM equation.
GCF(40,58) = 2
LCM(40,58) = ( 40 × 58) / 2
LCM(40,58) = 2320 / 2
LCM(40,58) = 1160
(i) The LCM of 58 and 40 is associative
LCM of 40 and 58 = LCM of 58 and 40
1. What is the LCM of 40 and 58?
Answer: LCM of 40 and 58 is 1160.
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 58?
Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.
4. How to Find the LCM of 40 and 58?
Answer:
Least Common Multiple of 40 and 58 = 1160
Step 1: Find the prime factorization of 40
40 = 2 x 2 x 2 x 5
Step 2: Find the prime factorization of 58
58 = 2 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1160 = 2 x 2 x 2 x 5 x 29
Step 4: Therefore, the least common multiple of 40 and 58 is 1160.