Advertisements
Advertisements
प्रश्न
A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?
Advertisements
उत्तर
Quantity of oil A = 120 liters
Quantity of oil B = 180 liters
uantity of oil C = 240 liters
We want to fill oils A, B and C in tins of the same capacity
∴ The greatest capacity of the tin chat can hold oil. A, B and C = HCF of 120, 180 and 240
By fundamental theorem of arithmetic
120 = 23 × 3 × 5
180 = 22 × 32 × 5
240 = 24 × 3 × 5
HCF = 22 × 3 × 5 = 4 × 3 × 5 = 60 liters
The greatest capacity of tin = 60 liters
APPEARS IN
संबंधित प्रश्न
Find the LCM and HCF of the following integers by applying the prime factorisation method.
12, 15 and 21
Determine the prime factorisation of each of the following positive integer:
45470971
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = Product of the two numbers.
26 and 91
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers. \[\frac{3}{8}\]
Write the exponent of 2 in the price factorization of 144.
Express the number as a product of its prime factor:
5005
Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field. Harish takes 12 minutes. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet?
Express 98 as a product of its primes.
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
For some integer m, every even integer is of the form ______.
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?
Show the 6n cannot end with digit 0 for any natural number 'n'.
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.
The prime factorisation of the number 2304 is ______.
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
