Least Common Multiple (LCM) of 101 and 165
The least common multiple (LCM) of 101 and 165 is 16665.
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 101 and 165?
First, calculate the GCD of 101 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 165 = 0 remainder 101 |
| 2 | 165 ÷ 101 = 1 remainder 64 |
| 3 | 101 ÷ 64 = 1 remainder 37 |
| 4 | 64 ÷ 37 = 1 remainder 27 |
| 5 | 37 ÷ 27 = 1 remainder 10 |
| 6 | 27 ÷ 10 = 2 remainder 7 |
| 7 | 10 ÷ 7 = 1 remainder 3 |
| 8 | 7 ÷ 3 = 2 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 59 | 5251 |
| 122 and 182 | 11102 |
| 34 and 66 | 1122 |
| 55 and 150 | 1650 |
| 51 and 10 | 510 |