Least Common Multiple (LCM) of 165 and 102
The least common multiple (LCM) of 165 and 102 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 165 and 102?
First, calculate the GCD of 165 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 102 = 1 remainder 63 |
| 2 | 102 ÷ 63 = 1 remainder 39 |
| 3 | 63 ÷ 39 = 1 remainder 24 |
| 4 | 39 ÷ 24 = 1 remainder 15 |
| 5 | 24 ÷ 15 = 1 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 83 | 7719 |
| 76 and 188 | 3572 |
| 115 and 16 | 1840 |
| 21 and 147 | 147 |
| 149 and 104 | 15496 |