Least Common Multiple (LCM) of 172 and 39
The least common multiple (LCM) of 172 and 39 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 172 and 39?
First, calculate the GCD of 172 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 39 = 4 remainder 16 |
| 2 | 39 ÷ 16 = 2 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 76 | 836 |
| 111 and 88 | 9768 |
| 12 and 171 | 684 |
| 114 and 117 | 4446 |
| 54 and 128 | 3456 |