Least Common Multiple (LCM) of 67 and 172
The least common multiple (LCM) of 67 and 172 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 67 and 172?
First, calculate the GCD of 67 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 172 = 0 remainder 67 |
| 2 | 172 ÷ 67 = 2 remainder 38 |
| 3 | 67 ÷ 38 = 1 remainder 29 |
| 4 | 38 ÷ 29 = 1 remainder 9 |
| 5 | 29 ÷ 9 = 3 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 196 | 1176 |
| 114 and 199 | 22686 |
| 51 and 85 | 255 |
| 53 and 71 | 3763 |
| 157 and 179 | 28103 |