Least Common Multiple (LCM) of 99 and 169
The least common multiple (LCM) of 99 and 169 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 99 and 169?
First, calculate the GCD of 99 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 169 = 0 remainder 99 |
| 2 | 169 ÷ 99 = 1 remainder 70 |
| 3 | 99 ÷ 70 = 1 remainder 29 |
| 4 | 70 ÷ 29 = 2 remainder 12 |
| 5 | 29 ÷ 12 = 2 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 106 | 9646 |
| 157 and 140 | 21980 |
| 77 and 118 | 9086 |
| 68 and 80 | 1360 |
| 87 and 17 | 1479 |