Question

What is the LCM of \[6\] and \[4\]?

Answer 1

Hint: From the given question we are asked to find the least common multiple of two given numbers. Here for this question we will use the prime factorisation method and find the factors for the two given numbers and then we find the least common multiple for the numbers given. So, we proceed with our solution as follows.

Complete step by step solution:
Generally, the prime factorisation which is breaking down a given number into its prime (meaning a number only divisible by itself and \[1\]) factors (meaning the numbers which you multiply in order to get a certain product).
The number six break down into \[3\] and \[2\]. Which cannot be further divided.
So, the factorisation will be as follows.
\[\Rightarrow 6=3\times 2\]
The number four break down into \[2\] and \[2\]. Which cannot be further divided.
So, the factorisation will be as follows.
 \[\Rightarrow 4=2\times 2\]
The, multiply the factors by the most amount of times they appear in either set of factors.
\[2\] appears only once in six’s factors, but twice in four’s factors;
Therefore we multiply \[2\] by \[2\] since twice is more than once. Now the only different number is \[3\], which appears once in six’s factors, so we multiply \[3\] by \[1\].
Now, we multiply all those chosen numbers together which gives us the LCM.
\[\Rightarrow LCM=2\times 2\times 3\times 1\]
\[\Rightarrow LCM=12\]

Note: Students should have good knowledge in the concept of prime factorisation and also the concept of LCM. If we take the two only one time and multiply together we get \[ LCM=2\times 3\times 1\] instead of \[ LCM=2\times 2\times 3\times 1\] it makes our solution wrong.