Least Common Multiple (LCM) of 172 and 38
The least common multiple (LCM) of 172 and 38 is 3268.
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 38?
First, calculate the GCD of 172 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 38 = 4 remainder 20 |
| 2 | 38 ÷ 20 = 1 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 44 | 2948 |
| 67 and 157 | 10519 |
| 90 and 112 | 5040 |
| 110 and 176 | 880 |
| 53 and 26 | 1378 |