Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 69 and 80 the smallest integer that is 5520 that is divisible by both numbers.
Least Common Multiple (LCM) of 69 and 80 is 5520.
LCM(69,80) = 5520
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 69 and 80. First we will calculate the prime factors of 69 and 80.
Prime Factorization of 69
3 | 69 |
23 | 23 |
1 |
Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:
69 = 31×231
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 69 and 80.
LCM(69,80) = 24×31×51×231
LCM(69,80) = 5520
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
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 69 and 80, than apply into the LCM equation.
GCF(69,80) = 1
LCM(69,80) = ( 69 × 80) / 1
LCM(69,80) = 5520 / 1
LCM(69,80) = 5520
(i) The LCM of 80 and 69 is associative
LCM of 69 and 80 = LCM of 80 and 69
1. What is the LCM of 69 and 80?
Answer: LCM of 69 and 80 is 5520.
2. What are the Factors of 69?
Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.
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 69 and 80?
Answer:
Least Common Multiple of 69 and 80 = 5520
Step 1: Find the prime factorization of 69
69 = 3 x 23
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 = 5520 = 2 x 2 x 2 x 2 x 3 x 5 x 23
Step 4: Therefore, the least common multiple of 69 and 80 is 5520.