Least Common Multiple (LCM) of 100 and 69
The least common multiple (LCM) of 100 and 69 is 6900.
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 69?
First, calculate the GCD of 100 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 69 = 1 remainder 31 |
| 2 | 69 ÷ 31 = 2 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 26 | 2522 |
| 58 and 166 | 4814 |
| 195 and 153 | 9945 |
| 133 and 114 | 798 |
| 72 and 142 | 5112 |