Least Common Multiple (LCM) of 27 and 42
The least common multiple (LCM) of 27 and 42 is 378.
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 27 and 42?
First, calculate the GCD of 27 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 42 = 0 remainder 27 |
| 2 | 42 ÷ 27 = 1 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 112 | 560 |
| 82 and 99 | 8118 |
| 67 and 112 | 7504 |
| 107 and 72 | 7704 |
| 137 and 165 | 22605 |