Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5 and 14 the smallest integer that is 70 that is divisible by both numbers.
Least Common Multiple (LCM) of 5 and 14 is 70.
LCM(5,14) = 70
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 5 and 14. First we will calculate the prime factors of 5 and 14.
Prime Factorization of 5
5 | 5 |
1 |
Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:
5 = 51
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
Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 14.
LCM(5,14) = 21×51×71
LCM(5,14) = 70
Factors of 5
List of positive integer factors of 5 that divides 5 without a remainder.
1, 5
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 14, than apply into the LCM equation.
GCF(5,14) = 1
LCM(5,14) = ( 5 × 14) / 1
LCM(5,14) = 70 / 1
LCM(5,14) = 70
(i) The LCM of 14 and 5 is associative
LCM of 5 and 14 = LCM of 14 and 5
1. What is the LCM of 5 and 14?
Answer: LCM of 5 and 14 is 70.
2. What are the Factors of 5?
Answer: Factors of 5 are 1, 5. There are 2 integers that are factors of 5. The greatest factor of 5 is 5.
3. 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.
4. How to Find the LCM of 5 and 14?
Answer:
Least Common Multiple of 5 and 14 = 70
Step 1: Find the prime factorization of 5
5 = 5
Step 2: Find the prime factorization of 14
14 = 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 70 = 2 x 5 x 7
Step 4: Therefore, the least common multiple of 5 and 14 is 70.