Least Common Multiple (LCM) of 155 and 65
The least common multiple (LCM) of 155 and 65 is 2015.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 155 and 65?
First, calculate the GCD of 155 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 65 = 2 remainder 25 |
| 2 | 65 ÷ 25 = 2 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 12 | 852 |
| 91 and 31 | 2821 |
| 128 and 107 | 13696 |
| 83 and 98 | 8134 |
| 79 and 80 | 6320 |