Least Common Multiple (LCM) of 27 and 142
The least common multiple (LCM) of 27 and 142 is 3834.
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 142?
First, calculate the GCD of 27 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 142 = 0 remainder 27 |
| 2 | 142 ÷ 27 = 5 remainder 7 |
| 3 | 27 ÷ 7 = 3 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 128 | 4480 |
| 105 and 127 | 13335 |
| 72 and 58 | 2088 |
| 126 and 195 | 8190 |
| 16 and 172 | 688 |