Advertisements
Advertisements
प्रश्न
Three measuring rods are 64 cm, 80 cm and 96 cm in length. Find the least length of cloth that can be measured an exact number of times, using any of the rods.
उत्तर
Length of the three measuring rods are 64cm, 80cm and 96cm, respectively.
∴ Length of cloth that can be measured an exact number of times = LCM (64, 80, 96)
Prime factorization:
64 = 26
80 = 24 × 5
96 = 25 × 3
∴ LCM = product of greatest power of each prime factor involved in the numbers = 26 × 3 × 5 = 960cm = 9.6m
Hence, the required length of cloth is 9.6m.
APPEARS IN
संबंधित प्रश्न
Define HOE of two positive integers and find the HCF of the following pair of numbers:
105 and 120
If the HCF of 657 and 963 is expressible in the form 657x + 963y − 15, find x.
Using prime factorization, find the HCF and LCM of 30, 72, 432 .
The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161, find the other.
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `171/800`
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.
(i) `9/35`
Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).
The smallest number by which \[\sqrt{27}\] should be multiplied so as to get a rational number is
If n is a natural number, then 92n − 42n is always divisible by ______.
Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.
[Hint: Any positive integer can be written in the form 5q, 5q + 1, 5q + 2, 5q + 3, 5q + 4].
