HCF and LCM
Q. Find the HCF of 48, 60, and 72.
Solution
The HCF of 48, 60, and 72 is 12, as it is the largest number that divides all three.
Correct Answer: B — 24
Q. Find the HCF of 48, 64, and 80.
Solution
The HCF of 48, 64, and 80 is 16, as it is the largest number that divides all three.
Correct Answer: B — 16
Q. Find the LCM of 6 and 8.
Solution
The LCM of 6 and 8 is 24, as it is the smallest number that is a multiple of both.
Correct Answer: A — 24
Q. Find the LCM of 9 and 15.
Solution
The LCM of 9 and 15 is 45, as it is the smallest number that is a multiple of both.
Correct Answer: A — 45
Q. If the HCF of two numbers is 1, what can be said about the numbers?
-
A.
They are even
-
B.
They are odd
-
C.
They are coprime
-
D.
They are multiples of each other
Solution
If the HCF is 1, the numbers are coprime, meaning they have no common factors other than 1.
Correct Answer: C — They are coprime
Q. If the HCF of two numbers is 15 and their LCM is 150, what is the product of the two numbers?
-
A.
225
-
B.
1500
-
C.
300
-
D.
75
Solution
The product of the two numbers is equal to the product of their HCF and LCM, which is 15 * 150 = 2250.
Correct Answer: B — 1500
Q. If the HCF of two numbers is equal to one of the numbers, what can be inferred?
-
A.
The numbers are equal
-
B.
One number is a multiple of the other
-
C.
The numbers are coprime
-
D.
The numbers are both prime
Solution
If the HCF is equal to one of the numbers, it means that one number is a multiple of the other.
Correct Answer: B — One number is a multiple of the other
Q. If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?
Solution
The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.
Correct Answer: A — 40
Q. If the LCM of two numbers is 36 and their HCF is 6, what is the product of the two numbers?
-
A.
72
-
B.
108
-
C.
216
-
D.
144
Solution
The product of the two numbers is LCM * HCF = 36 * 6 = 216.
Correct Answer: C — 216
Q. If the LCM of two numbers is 72 and one of the numbers is 8, what is the other number?
Solution
The other number can be found using the formula LCM(a, b) = (a * b) / HCF(a, b). Here, 72 = (8 * x) / HCF(8, x). The other number is 18.
Correct Answer: B — 18
Q. If the LCM of two numbers is 84 and one of the numbers is 12, what is the other number?
Solution
The other number can be found using the formula: LCM = (a * b) / HCF. Here, 84 = (12 * b) / HCF. The other number is 28.
Correct Answer: C — 28
Q. What is the HCF of 100 and 250?
Solution
The HCF of 100 and 250 is 50, as it is the largest number that divides both.
Correct Answer: A — 50
Q. What is the HCF of 14, 28, and 42?
Solution
The HCF of 14, 28, and 42 is 14, as it is the largest number that divides all three.
Correct Answer: A — 14
Q. What is the HCF of 24 and 36?
Solution
The HCF of 24 and 36 is 6, as it is the largest number that divides both.
Correct Answer: A — 6
Q. What is the HCF of 56, 98, and 42?
Solution
The HCF of 56, 98, and 42 is 14, as it is the largest number that divides all three.
Correct Answer: A — 14
Q. What is the HCF of 81 and 27?
Solution
The HCF of 81 and 27 is 27, as it is the largest number that divides both.
Correct Answer: A — 27
Q. What is the LCM of 12, 15, and 20?
-
A.
60
-
B.
120
-
C.
180
-
D.
240
Solution
The LCM of 12, 15, and 20 is 60, as it is the smallest number that is a multiple of all three.
Correct Answer: B — 120
Q. What is the LCM of 4 and 5?
Solution
The LCM of 4 and 5 is 20, as it is the smallest number that is a multiple of both.
Correct Answer: A — 10
Q. What is the LCM of 6 and 8?
Solution
The LCM of 6 and 8 is 24, as it is the smallest number that is a multiple of both.
Correct Answer: B — 24
Q. What is the LCM of 6, 8, and 12?
Solution
The LCM of 6, 8, and 12 is 24, as it is the smallest number that is a multiple of all three.
Correct Answer: A — 24
Q. What is the LCM of 8, 12, and 15?
Solution
The LCM of 8, 12, and 15 is 120, as it is the smallest number that is a multiple of all three.
Correct Answer: A — 120
Q. What is the LCM of 9 and 21?
Solution
The LCM of 9 and 21 is 63, as it is the smallest number that is a multiple of both.
Correct Answer: A — 63
Q. What is the relationship between HCF and LCM of two numbers a and b?
-
A.
HCF = a + b
-
B.
HCF * LCM = a * b
-
C.
HCF + LCM = a * b
-
D.
HCF - LCM = a - b
Solution
The relationship is HCF * LCM = a * b, which holds for any two integers a and b.
Correct Answer: B — HCF * LCM = a * b
Q. Which of the following pairs of numbers has an HCF of 10?
-
A.
20 and 30
-
B.
25 and 35
-
C.
40 and 50
-
D.
15 and 25
Solution
The HCF of 40 and 50 is 10, as it is the largest number that divides both.
Correct Answer: C — 40 and 50
Showing 1 to 24 of 24 (1 Pages)
