Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10 and 30 the smallest integer that is 30 that is divisible by both numbers.
Least Common Multiple (LCM) of 10 and 30 is 30.
LCM(10,30) = 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 10 and 30. First we will calculate the prime factors of 10 and 30.
Prime Factorization of 10
2 | 10 |
5 | 5 |
1 |
Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:
10 = 21×51
Prime Factorization of 30
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:
30 = 21×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 30.
LCM(10,30) = 21×31×51
LCM(10,30) = 30
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1, 2, 5, 10
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 30, than apply into the LCM equation.
GCF(10,30) = 10
LCM(10,30) = ( 10 × 30) / 10
LCM(10,30) = 300 / 10
LCM(10,30) = 30
(i) The LCM of 30 and 10 is associative
LCM of 10 and 30 = LCM of 30 and 10
1. What is the LCM of 10 and 30?
Answer: LCM of 10 and 30 is 30.
2. What are the Factors of 10?
Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.
3. What are the Factors of 30?
Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.
4. How to Find the LCM of 10 and 30?
Answer:
Least Common Multiple of 10 and 30 = 30
Step 1: Find the prime factorization of 10
10 = 2 x 5
Step 2: Find the prime factorization of 30
30 = 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 = 30 = 2 x 3 x 5
Step 4: Therefore, the least common multiple of 10 and 30 is 30.