The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2, the quotient is 33. Find the other number.
Share
Get Access to:
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Let’s assume that the two numbers are A and B.
We know that the HCF of A and B is 33. Therefore, we can write:
A = 33x B = 33y
where x and y are co-prime integers (i.e., they have no common factors other than 1).
We also know that the LCM of A and B is 264. Therefore, we can write:
LCM(A, B) = 264
Multiplying the values of A and B that we obtained above, we get:
A x B = (33x) x (33y) = 1089xy
Therefore, we can write:
LCM(A, B) = 264 = (HCF(A, B)) x (A/B) x B
Substituting the values of HCF(A, B) and A/B from the problem statement, we get:
264 = 33 x 33 x B/33
Simplifying, we get:
264 = 33B
B = 8
Substituting this value of B in the equation A x B = 1089xy, we get:
A x 8 = 1089xy
Substituting the value of A/B = 33, we get:
A = 33 x 8 = 264
Therefore, the two numbers are A = 264 and B = 8.