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 27 the smallest integer that is 378 that is divisible by both numbers.
Least Common Multiple (LCM) of 14 and 27 is 378.
LCM(14,27) = 378
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 27. First we will calculate the prime factors of 14 and 27.
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 27
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:
27 = 33
Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 27.
LCM(14,27) = 21×33×71
LCM(14,27) = 378
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1, 3, 9, 27
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 27, than apply into the LCM equation.
GCF(14,27) = 1
LCM(14,27) = ( 14 × 27) / 1
LCM(14,27) = 378 / 1
LCM(14,27) = 378
(i) The LCM of 27 and 14 is associative
LCM of 14 and 27 = LCM of 27 and 14
1. What is the LCM of 14 and 27?
Answer: LCM of 14 and 27 is 378.
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 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
4. How to Find the LCM of 14 and 27?
Answer:
Least Common Multiple of 14 and 27 = 378
Step 1: Find the prime factorization of 14
14 = 2 x 7
Step 2: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 378 = 2 x 3 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 14 and 27 is 378.