Least Common Multiple (LCM) of 150 and 27
The least common multiple (LCM) of 150 and 27 is 1350.
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 150 and 27?
First, calculate the GCD of 150 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 27 = 5 remainder 15 |
| 2 | 27 ÷ 15 = 1 remainder 12 |
| 3 | 15 ÷ 12 = 1 remainder 3 |
| 4 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 178 | 29726 |
| 21 and 55 | 1155 |
| 17 and 166 | 2822 |
| 48 and 77 | 3696 |
| 165 and 157 | 25905 |