Least Common Multiple (LCM) of 165 and 42
The least common multiple (LCM) of 165 and 42 is 2310.
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 42?
First, calculate the GCD of 165 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 42 = 3 remainder 39 |
| 2 | 42 ÷ 39 = 1 remainder 3 |
| 3 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 108 | 864 |
| 91 and 93 | 8463 |
| 59 and 119 | 7021 |
| 123 and 151 | 18573 |
| 102 and 56 | 2856 |