Least Common Multiple (LCM) of 40 and 172
The least common multiple (LCM) of 40 and 172 is 1720.
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 40 and 172?
First, calculate the GCD of 40 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 172 = 0 remainder 40 |
| 2 | 172 ÷ 40 = 4 remainder 12 |
| 3 | 40 ÷ 12 = 3 remainder 4 |
| 4 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 58 | 1218 |
| 187 and 16 | 2992 |
| 58 and 109 | 6322 |
| 144 and 45 | 720 |
| 187 and 54 | 10098 |