Least Common Multiple (LCM) of 172 and 59
The least common multiple (LCM) of 172 and 59 is 10148.
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 59?
First, calculate the GCD of 172 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 59 = 2 remainder 54 |
| 2 | 59 ÷ 54 = 1 remainder 5 |
| 3 | 54 ÷ 5 = 10 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 16 | 2000 |
| 88 and 21 | 1848 |
| 121 and 58 | 7018 |
| 103 and 15 | 1545 |
| 86 and 127 | 10922 |