Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 14 and 30 the smallest integer that is 210 that is divisible by both numbers.
Least Common Multiple (LCM) of 14 and 30 is 210.
LCM(14,30) = 210
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 14 and 30. First we will calculate the prime factors of 14 and 30.
Prime Factorization of 14
2 | 14 |
7 | 7 |
1 |
Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:
14 = 21×71
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 14 and 30.
LCM(14,30) = 21×31×51×71
LCM(14,30) = 210
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
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 14 and 30, than apply into the LCM equation.
GCF(14,30) = 2
LCM(14,30) = ( 14 × 30) / 2
LCM(14,30) = 420 / 2
LCM(14,30) = 210
(i) The LCM of 30 and 14 is associative
LCM of 14 and 30 = LCM of 30 and 14
1. What is the LCM of 14 and 30?
Answer: LCM of 14 and 30 is 210.
2. What are the Factors of 14?
Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.
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 14 and 30?
Answer:
Least Common Multiple of 14 and 30 = 210
Step 1: Find the prime factorization of 14
14 = 2 x 7
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 = 210 = 2 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 14 and 30 is 210.