Least Common Multiple (LCM) of 150 and 63
The least common multiple (LCM) of 150 and 63 is 3150.
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 63?
First, calculate the GCD of 150 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 63 = 2 remainder 24 |
| 2 | 63 ÷ 24 = 2 remainder 15 |
| 3 | 24 ÷ 15 = 1 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 67 | 9715 |
| 123 and 73 | 8979 |
| 14 and 107 | 1498 |
| 194 and 49 | 9506 |
| 119 and 120 | 14280 |