Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 15 and 89 the smallest integer that is 1335 that is divisible by both numbers.
Least Common Multiple (LCM) of 15 and 89 is 1335.
LCM(15,89) = 1335
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 15 and 89. First we will calculate the prime factors of 15 and 89.
Prime Factorization of 15
3 | 15 |
5 | 5 |
1 |
Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:
15 = 31×51
Prime Factorization of 89
89 | 89 |
1 |
Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:
89 = 891
Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 89.
LCM(15,89) = 31×51×891
LCM(15,89) = 1335
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5, 15
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1, 89
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 89, than apply into the LCM equation.
GCF(15,89) = 1
LCM(15,89) = ( 15 × 89) / 1
LCM(15,89) = 1335 / 1
LCM(15,89) = 1335
(i) The LCM of 89 and 15 is associative
LCM of 15 and 89 = LCM of 89 and 15
1. What is the LCM of 15 and 89?
Answer: LCM of 15 and 89 is 1335.
2. What are the Factors of 15?
Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.
3. What are the Factors of 89?
Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.
4. How to Find the LCM of 15 and 89?
Answer:
Least Common Multiple of 15 and 89 = 1335
Step 1: Find the prime factorization of 15
15 = 3 x 5
Step 2: Find the prime factorization of 89
89 = 89
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1335 = 3 x 5 x 89
Step 4: Therefore, the least common multiple of 15 and 89 is 1335.