Least Common Multiple (LCM) of 40 and 23
The least common multiple (LCM) of 40 and 23 is 920.
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 40 and 23?
First, calculate the GCD of 40 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 23 = 1 remainder 17 |
| 2 | 23 ÷ 17 = 1 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 145 | 3770 |
| 176 and 113 | 19888 |
| 171 and 106 | 18126 |
| 53 and 165 | 8745 |
| 173 and 21 | 3633 |