Least Common Multiple (LCM) of 172 and 42
The least common multiple (LCM) of 172 and 42 is 3612.
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 42?
First, calculate the GCD of 172 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 42 = 4 remainder 4 |
| 2 | 42 ÷ 4 = 10 remainder 2 |
| 3 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 102 | 8364 |
| 77 and 33 | 231 |
| 150 and 60 | 300 |
| 56 and 84 | 168 |
| 47 and 21 | 987 |