Least Common Multiple (LCM) of 105 and 101
The least common multiple (LCM) of 105 and 101 is 10605.
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 101?
First, calculate the GCD of 105 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 101 = 1 remainder 4 |
| 2 | 101 ÷ 4 = 25 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 78 | 4758 |
| 179 and 98 | 17542 |
| 66 and 162 | 1782 |
| 35 and 56 | 280 |
| 161 and 58 | 9338 |