Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 58 and 60 the smallest integer that is 1740 that is divisible by both numbers.
Least Common Multiple (LCM) of 58 and 60 is 1740.
LCM(58,60) = 1740
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 58 and 60. First we will calculate the prime factors of 58 and 60.
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
Prime Factorization of 60
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:
60 = 22×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 58 and 60.
LCM(58,60) = 22×31×51×291
LCM(58,60) = 1740
Factors of 58
List of positive integer factors of 58 that divides 58 without a remainder.
1, 2, 29, 58
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 58 and 60, than apply into the LCM equation.
GCF(58,60) = 2
LCM(58,60) = ( 58 × 60) / 2
LCM(58,60) = 3480 / 2
LCM(58,60) = 1740
(i) The LCM of 60 and 58 is associative
LCM of 58 and 60 = LCM of 60 and 58
1. What is the LCM of 58 and 60?
Answer: LCM of 58 and 60 is 1740.
2. 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.
3. What are the Factors of 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
4. How to Find the LCM of 58 and 60?
Answer:
Least Common Multiple of 58 and 60 = 1740
Step 1: Find the prime factorization of 58
58 = 2 x 29
Step 2: Find the prime factorization of 60
60 = 2 x 2 x 3 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 = 1740 = 2 x 2 x 3 x 5 x 29
Step 4: Therefore, the least common multiple of 58 and 60 is 1740.