Advertisements
Advertisements
Question
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
Options
10
100
504
2520
Advertisements
Solution
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
RELATED QUESTIONS
Check whether 6n can end with the digit 0 for any natural number n.
What is the HCF of the smallest prime number and the smallest composite number?
Determine the prime factorisation of each of the following positive integer:
58500
Determine the prime factorisation of each of the following positive integer:
45470971
Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.
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.\[\frac{13}{125}\]
Express the number as a product of its prime factor:
5005
Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers.
510 and 92
Find the L.C.M. and H.C.F. of 408 and 170 by applying the fundamental theorem of Arithmetic
Find the least number that is divisible by the first ten natural numbers
If two positive integers A and B can be expressed as A = xy3 and B = x4y2z; x, y being prime numbers then HCF (A, B) is ______.
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
When a number is divided by 7, its remainder is always ______.
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
Explain why 3 × 5 × 7 + 7 is a composite number.
Find the HCF and LCM of 72 and 120.
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.
If n is a natural number, then 8n cannot end with digit
