Least Common Multiple (LCM) of 142 and 67
The least common multiple (LCM) of 142 and 67 is 9514.
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 67?
First, calculate the GCD of 142 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 67 = 2 remainder 8 |
| 2 | 67 ÷ 8 = 8 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 54 | 1728 |
| 13 and 57 | 741 |
| 83 and 69 | 5727 |
| 195 and 31 | 6045 |
| 181 and 10 | 1810 |