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 26 the smallest integer that is 182 that is divisible by both numbers.
Least Common Multiple (LCM) of 14 and 26 is 182.
LCM(14,26) = 182
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 26. First we will calculate the prime factors of 14 and 26.
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 26
2 | 26 |
13 | 13 |
1 |
Prime factors of 26 are 2,13. Prime factorization of 26 in exponential form is:
26 = 21×131
Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 26.
LCM(14,26) = 21×71×131
LCM(14,26) = 182
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
Factors of 26
List of positive integer factors of 26 that divides 26 without a remainder.
1, 2, 13, 26
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 26, than apply into the LCM equation.
GCF(14,26) = 2
LCM(14,26) = ( 14 × 26) / 2
LCM(14,26) = 364 / 2
LCM(14,26) = 182
(i) The LCM of 26 and 14 is associative
LCM of 14 and 26 = LCM of 26 and 14
1. What is the LCM of 14 and 26?
Answer: LCM of 14 and 26 is 182.
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 26?
Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.
4. How to Find the LCM of 14 and 26?
Answer:
Least Common Multiple of 14 and 26 = 182
Step 1: Find the prime factorization of 14
14 = 2 x 7
Step 2: Find the prime factorization of 26
26 = 2 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 182 = 2 x 7 x 13
Step 4: Therefore, the least common multiple of 14 and 26 is 182.