Least Common Multiple (LCM) of 72 and 68
The least common multiple (LCM) of 72 and 68 is 1224.
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 68?
First, calculate the GCD of 72 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 68 = 1 remainder 4 |
| 2 | 68 ÷ 4 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 70 | 1890 |
| 31 and 106 | 3286 |
| 175 and 120 | 4200 |
| 131 and 167 | 21877 |
| 37 and 156 | 5772 |