Least Common Multiple (LCM) of 67 and 72
The least common multiple (LCM) of 67 and 72 is 4824.
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 72?
First, calculate the GCD of 67 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 72 = 0 remainder 67 |
| 2 | 72 ÷ 67 = 1 remainder 5 |
| 3 | 67 ÷ 5 = 13 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 45 | 7335 |
| 194 and 113 | 21922 |
| 10 and 101 | 1010 |
| 180 and 50 | 900 |
| 165 and 33 | 165 |