Least Common Multiple (LCM) of 106 and 100
The least common multiple (LCM) of 106 and 100 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 106 and 100?
First, calculate the GCD of 106 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 100 = 1 remainder 6 |
| 2 | 100 ÷ 6 = 16 remainder 4 |
| 3 | 6 ÷ 4 = 1 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 94 | 940 |
| 29 and 38 | 1102 |
| 39 and 159 | 2067 |
| 32 and 109 | 3488 |
| 19 and 24 | 456 |