Least Common Multiple (LCM) of 100 and 62
The least common multiple (LCM) of 100 and 62 is 3100.
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 62?
First, calculate the GCD of 100 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 62 = 1 remainder 38 |
| 2 | 62 ÷ 38 = 1 remainder 24 |
| 3 | 38 ÷ 24 = 1 remainder 14 |
| 4 | 24 ÷ 14 = 1 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 108 | 1836 |
| 54 and 104 | 2808 |
| 82 and 14 | 574 |
| 181 and 38 | 6878 |
| 106 and 68 | 3604 |