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 34 the smallest integer that is 238 that is divisible by both numbers.
Least Common Multiple (LCM) of 14 and 34 is 238.
LCM(14,34) = 238
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 34. First we will calculate the prime factors of 14 and 34.
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 34
2 | 34 |
17 | 17 |
1 |
Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:
34 = 21×171
Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 34.
LCM(14,34) = 21×71×171
LCM(14,34) = 238
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1, 2, 7, 14
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1, 2, 17, 34
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 34, than apply into the LCM equation.
GCF(14,34) = 2
LCM(14,34) = ( 14 × 34) / 2
LCM(14,34) = 476 / 2
LCM(14,34) = 238
(i) The LCM of 34 and 14 is associative
LCM of 14 and 34 = LCM of 34 and 14
1. What is the LCM of 14 and 34?
Answer: LCM of 14 and 34 is 238.
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 34?
Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.
4. How to Find the LCM of 14 and 34?
Answer:
Least Common Multiple of 14 and 34 = 238
Step 1: Find the prime factorization of 14
14 = 2 x 7
Step 2: Find the prime factorization of 34
34 = 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 238 = 2 x 7 x 17
Step 4: Therefore, the least common multiple of 14 and 34 is 238.