Least Common Multiple (LCM) of 61 and 165
The least common multiple (LCM) of 61 and 165 is 10065.
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 61 and 165?
First, calculate the GCD of 61 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 165 = 0 remainder 61 |
| 2 | 165 ÷ 61 = 2 remainder 43 |
| 3 | 61 ÷ 43 = 1 remainder 18 |
| 4 | 43 ÷ 18 = 2 remainder 7 |
| 5 | 18 ÷ 7 = 2 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 71 | 6248 |
| 52 and 24 | 312 |
| 108 and 24 | 216 |
| 152 and 23 | 3496 |
| 37 and 190 | 7030 |