Aptitude - H.C.F and L.C.M
21.
The L.C.M of two prime numbers x and y (x > y) is 161. The value of (3y − x) is
Answer
161 = 7 x 23. So, x = 23 and y =7
∴ 3y − x = (3 x 7 − 23) = −2
Answer :
Option AExplanation :
161 = 7 x 23. So, x = 23 and y =7
∴ 3y − x = (3 x 7 − 23) = −2
22.
The H.C.F and L.C.M of two numbers are 12 and 72 respectively. If the sum of the two numbers is 60, then one of the two numbers will be :
Answer
Let the numbers be 12a and 12b, where a and b are co-primes.
Then, 12a x 12b = 12 x 72 ⇒ ab = 6
Co-primes with product 6 are a = 2, b= 3
∴ Numbers are (12 x 2, 12 x 3), i.e. 24 and 36.
Answer :
Option BExplanation :
Let the numbers be 12a and 12b, where a and b are co-primes.
Then, 12a x 12b = 12 x 72 ⇒ ab = 6
Co-primes with product 6 are a = 2, b= 3
∴ Numbers are (12 x 2, 12 x 3), i.e. 24 and 36.
23.
Which of the following is a pair of co-primes ?
Answer
H.C.F. of 18 and 25 is 1.
∴ 18 and 25 are co-primes.
Answer :
Option BExplanation :
H.C.F. of 18 and 25 is 1.
∴ 18 and 25 are co-primes.
24.
L.C.M of (23 x 3 x 52 x 7), (24 x 32 x 5 x 72 x 11) and (2 x 33 x 54) is :
Answer
L.C.M = Product of terms with highest powers of 2, 3, 5, 7, 11
∴ L.C.M = (24 x 33 x 54 x 72 x 11)
Answer :
Option CExplanation :
L.C.M = Product of terms with highest powers of 2, 3, 5, 7, 11
∴ L.C.M = (24 x 33 x 54 x 72 x 11)
25.
The sum of two numbers is 528 and their H.C.F. is 33. The number of such pairs is :
Answer
Let the numbers be 33a and 33b, where a and b are co-primes.
Then, 33a + 33b = 528 ⇒ 33(a + b) = 528 ⇒ a + b = 16
∴ (a = 1, b = 15), (a = 3, b = 13), (a = 5, b = 11), (a = 7, b = 9)
Possible number of pairs = 4
Answer :
Option CExplanation :
Let the numbers be 33a and 33b, where a and b are co-primes.
Then, 33a + 33b = 528 ⇒ 33(a + b) = 528 ⇒ a + b = 16
∴ (a = 1, b = 15), (a = 3, b = 13), (a = 5, b = 11), (a = 7, b = 9)
Possible number of pairs = 4
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