the LCM and the HCF of 3-digit numbers a16 and 30b are 3672 and 18 respectively. find a and b
Answers
Answer: HCF (Highest Common Factor)
As the rules of mathematics dictate, the greatest common divisor or the g c d of two or more positive integers happens to be the largest positive integer that divides the numbers without leaving a remainder. For example, take 8 and 12. The H.C.F. of 8 and 12 will be 4 because the highest number that can divide both 8 and 12 is 4.
LCM (Least Common Multiple)
In arithmetic, the least common multiple or LCM of two numbers say a and b, is denoted as LCM (a ,b). And the LCM is the smallest or least positive integer that is divisible by both a and b. For example, let us take two positive integers 4 and 6.
Step-by-step explanation:
How to find HCF and LCM?
Here are the methods we can use to find the HCF and LCM of given numbers.
Prime factor method
Division method
Let us learn both methods, one by one.
Prime Factor for HCF
Take an example of finding the highest common factor of 144, 104 and 160.
Now let us write the prime factors of 144, 104 and 160.
144 = 2 × 2 × 2 × 2 × 3 × 3
104 = 2 × 2 × 2 × 13
160 = 2 × 2 × 2 × 2 × 2 × 5
The common factors of 144, 104 and 160 are 2 × 2 × 2 = 8
Therefore, HCF (144, 104, 160) = 8
by this method you can find the answer