Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3 and 14 the smallest integer that is 42 that is divisible by both numbers.
Least Common Multiple (LCM) of 3 and 14 is 42.
LCM(3,14) = 42
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 3 and 14. First we will calculate the prime factors of 3 and 14.
Prime Factorization of 3
3 | 3 |
1 |
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
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 3 and 14.
LCM(3,14) = 21×31×71
LCM(3,14) = 42
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1, 3
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 3 and 14, than apply into the LCM equation.
GCF(3,14) = 1
LCM(3,14) = ( 3 × 14) / 1
LCM(3,14) = 42 / 1
LCM(3,14) = 42
(i) The LCM of 14 and 3 is associative
LCM of 3 and 14 = LCM of 14 and 3
1. What is the LCM of 3 and 14?
Answer: LCM of 3 and 14 is 42.
2. What are the Factors of 3?
Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.
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 3 and 14?
Answer:
Least Common Multiple of 3 and 14 = 42
Step 1: Find the prime factorization of 3
3 = 3
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 = 42 = 2 x 3 x 7
Step 4: Therefore, the least common multiple of 3 and 14 is 42.