Least Common Multiple (LCM) of 23 and 72
The least common multiple (LCM) of 23 and 72 is 1656.
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 23 and 72?
First, calculate the GCD of 23 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 72 = 0 remainder 23 |
| 2 | 72 ÷ 23 = 3 remainder 3 |
| 3 | 23 ÷ 3 = 7 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 22 | 2200 |
| 106 and 80 | 4240 |
| 132 and 170 | 11220 |
| 101 and 117 | 11817 |
| 124 and 142 | 8804 |