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 33 the smallest integer that is 165 that is divisible by both numbers.
Least Common Multiple (LCM) of 15 and 33 is 165.
LCM(15,33) = 165
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 33. First we will calculate the prime factors of 15 and 33.
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 33
3 | 33 |
11 | 11 |
1 |
Prime factors of 33 are 3,11. Prime factorization of 33 in exponential form is:
33 = 31×111
Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 33.
LCM(15,33) = 31×51×111
LCM(15,33) = 165
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5, 15
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1, 3, 11, 33
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 33, than apply into the LCM equation.
GCF(15,33) = 3
LCM(15,33) = ( 15 × 33) / 3
LCM(15,33) = 495 / 3
LCM(15,33) = 165
(i) The LCM of 33 and 15 is associative
LCM of 15 and 33 = LCM of 33 and 15
1. What is the LCM of 15 and 33?
Answer: LCM of 15 and 33 is 165.
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 33?
Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.
4. How to Find the LCM of 15 and 33?
Answer:
Least Common Multiple of 15 and 33 = 165
Step 1: Find the prime factorization of 15
15 = 3 x 5
Step 2: Find the prime factorization of 33
33 = 3 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 165 = 3 x 5 x 11
Step 4: Therefore, the least common multiple of 15 and 33 is 165.