Advertisements
Advertisements
प्रश्न
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
पर्याय
10
100
504
2520
Advertisements
उत्तर
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is 2520.
Explanation:
Factors of numbers from 1 to 10
1 = 1
2 = 1 × 2
3 = 1 × 3
4 = 1 × 2 × 2
5 = 1 × 5
6 = 1 × 2 × 3
7 = 1 × 7
8 = 1 × 2 × 2 × 2
9 = 1 × 3 × 3
10 = 1 × 2 × 5
∴ LCM of numbers from 1 to 10
= LCM(1, 2, 3, 4, 5, 6, 7, 8, 9,10)
= 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7
= 2520
APPEARS IN
संबंधित प्रश्न
Express the number as a product of its prime factor:
140
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
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?
State fundamental theorem of arithmetic.
Find the LCM and HCF of the following integers by applying the prime factorisation method:
40, 36 and 126
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.
\[\frac{13}{125}\]
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.
\[\frac{129}{2^2 \times 5^7}\]
If the prime factorization of a natural number n is 23 × 32 × 52 × 7, write the number of consecutive zeros in n.
Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic
What is the smallest number that when divided by three numbers such as 35, 56 and 91 leaves remainder 7 in each case?
The sum of the exponents of the prime factors in the prime factorization of 1729 is
LCM of the given number ‘x’ and ‘y’ where y is a multiple of ‘x’ is given by ______.
Explain why 3 × 5 × 7 + 7 is a composite number.
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) = pmqn and LCM (a, b) = prqs, then (m + n)(r + s) = ______.
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:
|
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. |
Based on the above information, answer the following questions:
- How many guests Khushi can invite at the most?
- How many apples and bananas will each guest get?
-
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
OR - 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.
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
