Least Common Multiple (LCM) of 169 and 99
The least common multiple (LCM) of 169 and 99 is 16731.
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 169 and 99?
First, calculate the GCD of 169 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 99 = 1 remainder 70 |
| 2 | 99 ÷ 70 = 1 remainder 29 |
| 3 | 70 ÷ 29 = 2 remainder 12 |
| 4 | 29 ÷ 12 = 2 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 97 | 9215 |
| 72 and 57 | 1368 |
| 123 and 18 | 738 |
| 133 and 89 | 11837 |
| 96 and 23 | 2208 |