Least Common Multiple (LCM) of 46 and 72
The least common multiple (LCM) of 46 and 72 is 1656.
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 46 and 72?
First, calculate the GCD of 46 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 72 = 0 remainder 46 |
| 2 | 72 ÷ 46 = 1 remainder 26 |
| 3 | 46 ÷ 26 = 1 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 107 | 11235 |
| 152 and 72 | 1368 |
| 174 and 55 | 9570 |
| 18 and 109 | 1962 |
| 96 and 170 | 8160 |