Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 50 and 80 the smallest integer that is 400 that is divisible by both numbers.
Least Common Multiple (LCM) of 50 and 80 is 400.
LCM(50,80) = 400
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 50 and 80. First we will calculate the prime factors of 50 and 80.
Prime Factorization of 50
2 | 50 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 50 are 2,5. Prime factorization of 50 in exponential form is:
50 = 21×52
Prime Factorization of 80
2 | 80 |
2 | 40 |
2 | 20 |
2 | 10 |
5 | 5 |
1 |
Prime factors of 80 are 2,5. Prime factorization of 80 in exponential form is:
80 = 24×51
Now multiplying the highest exponent prime factors to calculate the LCM of 50 and 80.
LCM(50,80) = 24×52
LCM(50,80) = 400
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1, 2, 5, 10, 25, 50
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 50 and 80, than apply into the LCM equation.
GCF(50,80) = 10
LCM(50,80) = ( 50 × 80) / 10
LCM(50,80) = 4000 / 10
LCM(50,80) = 400
(i) The LCM of 80 and 50 is associative
LCM of 50 and 80 = LCM of 80 and 50
1. What is the LCM of 50 and 80?
Answer: LCM of 50 and 80 is 400.
2. What are the Factors of 50?
Answer: Factors of 50 are 1, 2, 5, 10, 25, 50. There are 6 integers that are factors of 50. The greatest factor of 50 is 50.
3. What are the Factors of 80?
Answer: Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. There are 10 integers that are factors of 80. The greatest factor of 80 is 80.
4. How to Find the LCM of 50 and 80?
Answer:
Least Common Multiple of 50 and 80 = 400
Step 1: Find the prime factorization of 50
50 = 2 x 5 x 5
Step 2: Find the prime factorization of 80
80 = 2 x 2 x 2 x 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 400 = 2 x 2 x 2 x 2 x 5 x 5
Step 4: Therefore, the least common multiple of 50 and 80 is 400.