Least Common Multiple (LCM) of 99 and 174
The least common multiple (LCM) of 99 and 174 is 5742.
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 174?
First, calculate the GCD of 99 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 174 = 0 remainder 99 |
| 2 | 174 ÷ 99 = 1 remainder 75 |
| 3 | 99 ÷ 75 = 1 remainder 24 |
| 4 | 75 ÷ 24 = 3 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 105 | 1785 |
| 38 and 172 | 3268 |
| 65 and 88 | 5720 |
| 150 and 67 | 10050 |
| 124 and 139 | 17236 |