Least Common Multiple (LCM) of 101 and 106
The least common multiple (LCM) of 101 and 106 is 10706.
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 106?
First, calculate the GCD of 101 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 106 = 0 remainder 101 |
| 2 | 106 ÷ 101 = 1 remainder 5 |
| 3 | 101 ÷ 5 = 20 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 80 | 560 |
| 151 and 82 | 12382 |
| 181 and 37 | 6697 |
| 79 and 81 | 6399 |
| 137 and 168 | 23016 |