Least Common Multiple (LCM) of 172 and 67
The least common multiple (LCM) of 172 and 67 is 11524.
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 67?
First, calculate the GCD of 172 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 67 = 2 remainder 38 |
| 2 | 67 ÷ 38 = 1 remainder 29 |
| 3 | 38 ÷ 29 = 1 remainder 9 |
| 4 | 29 ÷ 9 = 3 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 39 | 3822 |
| 152 and 36 | 1368 |
| 19 and 136 | 2584 |
| 150 and 116 | 8700 |
| 104 and 175 | 18200 |