Least Common Multiple (LCM) of 100 and 106
The least common multiple (LCM) of 100 and 106 is 5300.
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 100 and 106?
First, calculate the GCD of 100 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 106 = 0 remainder 100 |
| 2 | 106 ÷ 100 = 1 remainder 6 |
| 3 | 100 ÷ 6 = 16 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 115 | 1150 |
| 67 and 175 | 11725 |
| 31 and 122 | 3782 |
| 132 and 81 | 3564 |
| 68 and 171 | 11628 |