Least Common Multiple (LCM) of 150 and 55
The least common multiple (LCM) of 150 and 55 is 1650.
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 55?
First, calculate the GCD of 150 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 55 = 2 remainder 40 |
| 2 | 55 ÷ 40 = 1 remainder 15 |
| 3 | 40 ÷ 15 = 2 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 16 | 560 |
| 84 and 99 | 2772 |
| 21 and 148 | 3108 |
| 170 and 58 | 4930 |
| 11 and 109 | 1199 |