Least Common Multiple (LCM) of 43 and 156
The least common multiple (LCM) of 43 and 156 is 6708.
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 43 and 156?
First, calculate the GCD of 43 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 156 = 0 remainder 43 |
| 2 | 156 ÷ 43 = 3 remainder 27 |
| 3 | 43 ÷ 27 = 1 remainder 16 |
| 4 | 27 ÷ 16 = 1 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 143 | 16016 |
| 128 and 198 | 12672 |
| 178 and 53 | 9434 |
| 113 and 88 | 9944 |
| 67 and 93 | 6231 |