Least Common Multiple (LCM) of 152 and 174
The least common multiple (LCM) of 152 and 174 is 13224.
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 152 and 174?
First, calculate the GCD of 152 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 174 = 0 remainder 152 |
| 2 | 174 ÷ 152 = 1 remainder 22 |
| 3 | 152 ÷ 22 = 6 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 103 | 14214 |
| 41 and 189 | 7749 |
| 55 and 75 | 825 |
| 159 and 128 | 20352 |
| 127 and 36 | 4572 |