Least Common Multiple (LCM) of 105 and 50
The least common multiple (LCM) of 105 and 50 is 1050.
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 105 and 50?
First, calculate the GCD of 105 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 50 = 2 remainder 5 |
| 2 | 50 ÷ 5 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 58 | 5858 |
| 34 and 167 | 5678 |
| 13 and 17 | 221 |
| 65 and 182 | 910 |
| 73 and 42 | 3066 |