Least Common Multiple (LCM) of 101 and 105
The least common multiple (LCM) of 101 and 105 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 101 and 105?
First, calculate the GCD of 101 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 105 = 0 remainder 101 |
| 2 | 105 ÷ 101 = 1 remainder 4 |
| 3 | 101 ÷ 4 = 25 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 32 | 5280 |
| 160 and 66 | 5280 |
| 21 and 93 | 651 |
| 163 and 176 | 28688 |
| 86 and 52 | 2236 |