Least Common Multiple (LCM) of 172 and 140
The least common multiple (LCM) of 172 and 140 is 6020.
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 140?
First, calculate the GCD of 172 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 140 = 1 remainder 32 |
| 2 | 140 ÷ 32 = 4 remainder 12 |
| 3 | 32 ÷ 12 = 2 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 126 | 126 |
| 44 and 121 | 484 |
| 138 and 25 | 3450 |
| 110 and 98 | 5390 |
| 77 and 50 | 3850 |