Least Common Multiple (LCM) of 152 and 90
The least common multiple (LCM) of 152 and 90 is 6840.
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 90?
First, calculate the GCD of 152 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 90 = 1 remainder 62 |
| 2 | 90 ÷ 62 = 1 remainder 28 |
| 3 | 62 ÷ 28 = 2 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 120 | 2760 |
| 46 and 28 | 644 |
| 163 and 149 | 24287 |
| 14 and 31 | 434 |
| 131 and 56 | 7336 |