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 |
|---|---|
| 144 and 14 | 1008 |
| 141 and 119 | 16779 |
| 113 and 95 | 10735 |
| 148 and 159 | 23532 |
| 127 and 142 | 18034 |