Least Common Multiple (LCM) of 100 and 61
The least common multiple (LCM) of 100 and 61 is 6100.
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 61?
First, calculate the GCD of 100 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 61 = 1 remainder 39 |
| 2 | 61 ÷ 39 = 1 remainder 22 |
| 3 | 39 ÷ 22 = 1 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 18 | 306 |
| 55 and 64 | 3520 |
| 192 and 12 | 192 |
| 129 and 85 | 10965 |
| 52 and 143 | 572 |