Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2 and 15 the smallest integer that is 30 that is divisible by both numbers.
Least Common Multiple (LCM) of 2 and 15 is 30.
LCM(2,15) = 30
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 2 and 15. First we will calculate the prime factors of 2 and 15.
Prime Factorization of 2
2 | 2 |
1 |
Prime factors of 2 are 2. Prime factorization of 2 in exponential form is:
2 = 21
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
Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 15.
LCM(2,15) = 21×31×51
LCM(2,15) = 30
Factors of 2
List of positive integer factors of 2 that divides 2 without a remainder.
1, 2
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5, 15
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 15, than apply into the LCM equation.
GCF(2,15) = 1
LCM(2,15) = ( 2 × 15) / 1
LCM(2,15) = 30 / 1
LCM(2,15) = 30
(i) The LCM of 15 and 2 is associative
LCM of 2 and 15 = LCM of 15 and 2
1. What is the LCM of 2 and 15?
Answer: LCM of 2 and 15 is 30.
2. What are the Factors of 2?
Answer: Factors of 2 are 1, 2. There are 2 integers that are factors of 2. The greatest factor of 2 is 2.
3. 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.
4. How to Find the LCM of 2 and 15?
Answer:
Least Common Multiple of 2 and 15 = 30
Step 1: Find the prime factorization of 2
2 = 2
Step 2: Find the prime factorization of 15
15 = 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 = 30 = 2 x 3 x 5
Step 4: Therefore, the least common multiple of 2 and 15 is 30.