Least Common Multiple (LCM) of 62 and 100
The least common multiple (LCM) of 62 and 100 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 62 and 100?
First, calculate the GCD of 62 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 62 ÷ 100 = 0 remainder 62 |
| 2 | 100 ÷ 62 = 1 remainder 38 |
| 3 | 62 ÷ 38 = 1 remainder 24 |
| 4 | 38 ÷ 24 = 1 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 49 | 147 |
| 118 and 145 | 17110 |
| 24 and 97 | 2328 |
| 138 and 120 | 2760 |
| 74 and 116 | 4292 |