Least Common Multiple of 34 and 42
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 34 and 42 the smallest integer that is 714 that is divisible by both numbers.
Least Common Multiple (LCM) of 34 and 42 is 714.
LCM(34,42) = 714
LCM of 34 and 42
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 34 and 42 by Prime method
- Least Common Multiple of 34 and 42 with GCF Formula
LCM of 34 and 42 is 714
Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 42. First we will calculate the prime factors of 34 and 42.
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
Prime Factorization of 42
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 42 are 2, 3,7. Prime factorization of 42 in exponential form is:
42 = 21×31×71
Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 42.
LCM(34,42) = 21×31×71×171
LCM(34,42) = 714
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1, 2, 17, 34
Factors of 42
List of positive integer factors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42
Least Common Multiple of 34 and 42 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 42, than apply into the LCM equation.
GCF(34,42) = 2
LCM(34,42) = ( 34 × 42) / 2
LCM(34,42) = 1428 / 2
LCM(34,42) = 714
Properties of LCM 34 and 42
(i) The LCM of 42 and 34 is associative
LCM of 34 and 42 = LCM of 42 and 34
Related Least Common Multiples of 34
Related Least Common Multiples of 42
Frequently Asked Questions on LCM of 34 and 42
1. What is the LCM of 34 and 42?
Answer: LCM of 34 and 42 is 714.
2. 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.
3. What are the Factors of 42?
Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.
4. How to Find the LCM of 34 and 42?
Answer:
Least Common Multiple of 34 and 42 = 714
Step 1: Find the prime factorization of 34
34 = 2 x 17
Step 2: Find the prime factorization of 42
42 = 2 x 3 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 = 714 = 2 x 3 x 7 x 17
Step 4: Therefore, the least common multiple of 34 and 42 is 714.