Least Common Multiple (LCM) of 172 and 142
The least common multiple (LCM) of 172 and 142 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 172 and 142?
First, calculate the GCD of 172 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 142 = 1 remainder 30 |
| 2 | 142 ÷ 30 = 4 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 167 | 11356 |
| 160 and 79 | 12640 |
| 160 and 67 | 10720 |
| 126 and 31 | 3906 |
| 87 and 110 | 9570 |