Least Common Multiple (LCM) of 174 and 136
The least common multiple (LCM) of 174 and 136 is 11832.
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 174 and 136?
First, calculate the GCD of 174 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 136 = 1 remainder 38 |
| 2 | 136 ÷ 38 = 3 remainder 22 |
| 3 | 38 ÷ 22 = 1 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 45 | 180 |
| 67 and 192 | 12864 |
| 99 and 97 | 9603 |
| 97 and 120 | 11640 |
| 39 and 85 | 3315 |