Least Common Multiple (LCM) of 100 and 71
The least common multiple (LCM) of 100 and 71 is 7100.
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 71?
First, calculate the GCD of 100 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 71 = 1 remainder 29 |
| 2 | 71 ÷ 29 = 2 remainder 13 |
| 3 | 29 ÷ 13 = 2 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 125 | 21750 |
| 186 and 106 | 9858 |
| 14 and 155 | 2170 |
| 16 and 122 | 976 |
| 66 and 74 | 2442 |