Least Common Multiple (LCM) of 42 and 66
The least common multiple (LCM) of 42 and 66 is 462.
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 66?
First, calculate the GCD of 42 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 66 = 0 remainder 42 |
| 2 | 66 ÷ 42 = 1 remainder 24 |
| 3 | 42 ÷ 24 = 1 remainder 18 |
| 4 | 24 ÷ 18 = 1 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 192 | 5568 |
| 170 and 192 | 16320 |
| 19 and 30 | 570 |
| 45 and 72 | 360 |
| 12 and 18 | 36 |