Least Common Multiple (LCM) of 42 and 23
The least common multiple (LCM) of 42 and 23 is 966.
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 42 and 23?
First, calculate the GCD of 42 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 23 = 1 remainder 19 |
| 2 | 23 ÷ 19 = 1 remainder 4 |
| 3 | 19 ÷ 4 = 4 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 29 | 3306 |
| 147 and 52 | 7644 |
| 159 and 97 | 15423 |
| 108 and 37 | 3996 |
| 176 and 45 | 7920 |