Least Common Multiple (LCM) of 45 and 152
The least common multiple (LCM) of 45 and 152 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 45 and 152?
First, calculate the GCD of 45 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 152 = 0 remainder 45 |
| 2 | 152 ÷ 45 = 3 remainder 17 |
| 3 | 45 ÷ 17 = 2 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 176 | 13200 |
| 174 and 70 | 6090 |
| 93 and 132 | 4092 |
| 161 and 164 | 26404 |
| 165 and 124 | 20460 |