Least Common Multiple (LCM) of 100 and 105
The least common multiple (LCM) of 100 and 105 is 2100.
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 105?
First, calculate the GCD of 100 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 105 = 0 remainder 100 |
| 2 | 105 ÷ 100 = 1 remainder 5 |
| 3 | 100 ÷ 5 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 80 | 13040 |
| 61 and 18 | 1098 |
| 119 and 49 | 833 |
| 50 and 174 | 4350 |
| 188 and 63 | 11844 |