Least Common Multiple (LCM) of 150 and 84
The least common multiple (LCM) of 150 and 84 is 2100.
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 84?
First, calculate the GCD of 150 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 84 = 1 remainder 66 |
| 2 | 84 ÷ 66 = 1 remainder 18 |
| 3 | 66 ÷ 18 = 3 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 168 | 3864 |
| 106 and 64 | 3392 |
| 90 and 53 | 4770 |
| 171 and 59 | 10089 |
| 129 and 120 | 5160 |