Least Common Multiple (LCM) of 153 and 174
The least common multiple (LCM) of 153 and 174 is 8874.
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 153 and 174?
First, calculate the GCD of 153 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 174 = 0 remainder 153 |
| 2 | 174 ÷ 153 = 1 remainder 21 |
| 3 | 153 ÷ 21 = 7 remainder 6 |
| 4 | 21 ÷ 6 = 3 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 98 | 9702 |
| 130 and 15 | 390 |
| 129 and 129 | 129 |
| 52 and 144 | 1872 |
| 23 and 70 | 1610 |