Least Common Multiple (LCM) of 102 and 165
The least common multiple (LCM) of 102 and 165 is 5610.
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 102 and 165?
First, calculate the GCD of 102 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 165 = 0 remainder 102 |
| 2 | 165 ÷ 102 = 1 remainder 63 |
| 3 | 102 ÷ 63 = 1 remainder 39 |
| 4 | 63 ÷ 39 = 1 remainder 24 |
| 5 | 39 ÷ 24 = 1 remainder 15 |
| 6 | 24 ÷ 15 = 1 remainder 9 |
| 7 | 15 ÷ 9 = 1 remainder 6 |
| 8 | 9 ÷ 6 = 1 remainder 3 |
| 9 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 152 | 3344 |
| 10 and 134 | 670 |
| 172 and 109 | 18748 |
| 113 and 67 | 7571 |
| 72 and 151 | 10872 |