Least Common Multiple (LCM) of 142 and 172
The least common multiple (LCM) of 142 and 172 is 12212.
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 172?
First, calculate the GCD of 142 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 172 = 0 remainder 142 |
| 2 | 172 ÷ 142 = 1 remainder 30 |
| 3 | 142 ÷ 30 = 4 remainder 22 |
| 4 | 30 ÷ 22 = 1 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 20 | 540 |
| 140 and 154 | 1540 |
| 109 and 62 | 6758 |
| 55 and 77 | 385 |
| 148 and 78 | 5772 |