Least Common Multiple (LCM) of 42 and 165
The least common multiple (LCM) of 42 and 165 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 42 and 165?
First, calculate the GCD of 42 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 165 = 0 remainder 42 |
| 2 | 165 ÷ 42 = 3 remainder 39 |
| 3 | 42 ÷ 39 = 1 remainder 3 |
| 4 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 119 | 119 |
| 121 and 121 | 121 |
| 85 and 160 | 2720 |
| 26 and 13 | 26 |
| 165 and 109 | 17985 |