Least Common Multiple (LCM) of 39 and 172
The least common multiple (LCM) of 39 and 172 is 6708.
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 39 and 172?
First, calculate the GCD of 39 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 172 = 0 remainder 39 |
| 2 | 172 ÷ 39 = 4 remainder 16 |
| 3 | 39 ÷ 16 = 2 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 57 | 3420 |
| 145 and 119 | 17255 |
| 12 and 111 | 444 |
| 34 and 59 | 2006 |
| 166 and 79 | 13114 |