Least Common Multiple (LCM) of 152 and 178
The least common multiple (LCM) of 152 and 178 is 13528.
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 178?
First, calculate the GCD of 152 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 178 = 0 remainder 152 |
| 2 | 178 ÷ 152 = 1 remainder 26 |
| 3 | 152 ÷ 26 = 5 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 30 | 5370 |
| 38 and 142 | 2698 |
| 82 and 155 | 12710 |
| 117 and 36 | 468 |
| 182 and 115 | 20930 |