Least Common Multiple (LCM) of 72 and 164
The least common multiple (LCM) of 72 and 164 is 2952.
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 164?
First, calculate the GCD of 72 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 164 = 0 remainder 72 |
| 2 | 164 ÷ 72 = 2 remainder 20 |
| 3 | 72 ÷ 20 = 3 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 31 | 2480 |
| 180 and 192 | 2880 |
| 194 and 66 | 6402 |
| 67 and 61 | 4087 |
| 165 and 123 | 6765 |