Least Common Multiple (LCM) of 142 and 165
The least common multiple (LCM) of 142 and 165 is 23430.
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 142 and 165?
First, calculate the GCD of 142 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 165 = 0 remainder 142 |
| 2 | 165 ÷ 142 = 1 remainder 23 |
| 3 | 142 ÷ 23 = 6 remainder 4 |
| 4 | 23 ÷ 4 = 5 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 64 | 2496 |
| 52 and 190 | 4940 |
| 98 and 71 | 6958 |
| 64 and 189 | 12096 |
| 103 and 185 | 19055 |