Least Common Multiple (LCM) of 100 and 141
The least common multiple (LCM) of 100 and 141 is 14100.
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 141?
First, calculate the GCD of 100 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 141 = 0 remainder 100 |
| 2 | 141 ÷ 100 = 1 remainder 41 |
| 3 | 100 ÷ 41 = 2 remainder 18 |
| 4 | 41 ÷ 18 = 2 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 198 | 3762 |
| 63 and 158 | 9954 |
| 194 and 22 | 2134 |
| 102 and 55 | 5610 |
| 105 and 121 | 12705 |