Least Common Multiple (LCM) of 172 and 72
The least common multiple (LCM) of 172 and 72 is 3096.
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 72?
First, calculate the GCD of 172 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 72 = 2 remainder 28 |
| 2 | 72 ÷ 28 = 2 remainder 16 |
| 3 | 28 ÷ 16 = 1 remainder 12 |
| 4 | 16 ÷ 12 = 1 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 91 | 12558 |
| 35 and 17 | 595 |
| 41 and 150 | 6150 |
| 127 and 60 | 7620 |
| 83 and 67 | 5561 |