English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF (a, b) = p^mqⁿ and LCM (a, b) = p^rq^s, then (m + n)(r + s) = ______.

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.

Find the HCF and LCM of 26, 65 and 117, using prime factorisation.

The LCM of smallest 2-digit number and smallest composite number is ______.

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Assertion (A): The HCF of two numbers is 5 and their product is 150. Then their LCM is 40.

Reason(R): For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.

(HCF × LCM) for the numbers 70 and 40 is ______.

Read the following passage:

Based on the above information, answer the following questions:

1. How many guests Khushi can invite at the most?
2. How many apples and bananas will each guest get?
3. 1. If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
      OR
   2. If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
      

(HCF × LCM) for the numbers 30 and 70 is ______.

If HCF (72, 120) = 24, then LCM (72, 120) is ______.

The prime factorisation of the number 2304 is ______.

If n is a natural number, then 8ⁿ cannot end with digit

The HCF of the smallest 2-digit number and the smallest composite number is ______.

The mean of first ten natural numbers is ______.