Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 20 and 29 the smallest integer that is 580 that is divisible by both numbers.
Least Common Multiple (LCM) of 20 and 29 is 580.
LCM(20,29) = 580
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 20 and 29. First we will calculate the prime factors of 20 and 29.
Prime Factorization of 20
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:
20 = 22×51
Prime Factorization of 29
29 | 29 |
1 |
Prime factors of 29 are 29. Prime factorization of 29 in exponential form is:
29 = 291
Now multiplying the highest exponent prime factors to calculate the LCM of 20 and 29.
LCM(20,29) = 22×51×291
LCM(20,29) = 580
Factors of 20
List of positive integer factors of 20 that divides 20 without a remainder.
1, 2, 4, 5, 10, 20
Factors of 29
List of positive integer factors of 29 that divides 29 without a remainder.
1, 29
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 29, than apply into the LCM equation.
GCF(20,29) = 1
LCM(20,29) = ( 20 × 29) / 1
LCM(20,29) = 580 / 1
LCM(20,29) = 580
(i) The LCM of 29 and 20 is associative
LCM of 20 and 29 = LCM of 29 and 20
1. What is the LCM of 20 and 29?
Answer: LCM of 20 and 29 is 580.
2. What are the Factors of 20?
Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.
3. What are the Factors of 29?
Answer: Factors of 29 are 1, 29. There are 2 integers that are factors of 29. The greatest factor of 29 is 29.
4. How to Find the LCM of 20 and 29?
Answer:
Least Common Multiple of 20 and 29 = 580
Step 1: Find the prime factorization of 20
20 = 2 x 2 x 5
Step 2: Find the prime factorization of 29
29 = 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 580 = 2 x 2 x 5 x 29
Step 4: Therefore, the least common multiple of 20 and 29 is 580.