924
Determine the Value of Number p
We are given that when number p is divided by 55, the quotient is 4 and the remainder is 0.
Using the division algorithm, dividend = divisor × quotient + remainder, we can find p:
\(p = 55 \times 4 + 0\)
\(p = 220\)
Apply HCF and LCM Relationship
For any two positive integers, the product of the numbers is equal to the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM).
The formula is: HCF(p, q) × LCM(p, q) = p × q
We are given:
- HCF(p, q) = 44
- LCM(p, q) = 4620
- p = 220
Calculate the Value of Number q
Substitute the known values into the formula:
\(44 \times 4620 = 220 \times q\)
Now, solve for q:
\(q = \frac{44 \times 4620}{220}\)
To simplify, we can divide 44 by 220:
\(\frac{44}{220} = \frac{1}{5}\)
So the equation becomes:
\(q = \frac{1}{5} \times 4620\)
\(q = \frac{4620}{5}\)
\(q = 924\)
The calculated value for q is 924. Based on the provided options, the correct answer is Option C.
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
