Least Common Multiple (LCM) of 72 and 167
The least common multiple (LCM) of 72 and 167 is 12024.
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 72 and 167?
First, calculate the GCD of 72 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 167 = 0 remainder 72 |
| 2 | 167 ÷ 72 = 2 remainder 23 |
| 3 | 72 ÷ 23 = 3 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 64 | 4928 |
| 144 and 182 | 13104 |
| 18 and 57 | 342 |
| 123 and 180 | 7380 |
| 156 and 150 | 3900 |