Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 21 and 34 the smallest integer that is 714 that is divisible by both numbers.
Least Common Multiple (LCM) of 21 and 34 is 714.
LCM(21,34) = 714
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 21 and 34. First we will calculate the prime factors of 21 and 34.
Prime Factorization of 21
3 | 21 |
7 | 7 |
1 |
Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:
21 = 31×71
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 21 and 34.
LCM(21,34) = 21×31×71×171
LCM(21,34) = 714
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1, 3, 7, 21
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 21 and 34, than apply into the LCM equation.
GCF(21,34) = 1
LCM(21,34) = ( 21 × 34) / 1
LCM(21,34) = 714 / 1
LCM(21,34) = 714
(i) The LCM of 34 and 21 is associative
LCM of 21 and 34 = LCM of 34 and 21
1. What is the LCM of 21 and 34?
Answer: LCM of 21 and 34 is 714.
2. What are the Factors of 21?
Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.
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 21 and 34?
Answer:
Least Common Multiple of 21 and 34 = 714
Step 1: Find the prime factorization of 21
21 = 3 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 = 714 = 2 x 3 x 7 x 17
Step 4: Therefore, the least common multiple of 21 and 34 is 714.