Least Common Multiple (LCM) of 105 and 63
The least common multiple (LCM) of 105 and 63 is 315.
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 63?
First, calculate the GCD of 105 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 63 = 1 remainder 42 |
| 2 | 63 ÷ 42 = 1 remainder 21 |
| 3 | 42 ÷ 21 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 81 | 13041 |
| 108 and 80 | 2160 |
| 20 and 142 | 1420 |
| 76 and 27 | 2052 |
| 86 and 44 | 1892 |