Advertisements
Advertisements
प्रश्न
Find the greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36?
Advertisements
उत्तर
To find L.C.M. of 24, 15, 36
24 = 23 × 3
15 = 3 × 5
36 = 22 × 32
| Prime factors of 24, 15, 36 |
Greatest Exponents |
| 2 | 3 |
| 3 | 2 |
| 5 | 1 |
∴ L.C.M. = 23 × 32 × 51
= 8 × 9 × 5
= 360
If a number has to be exactly divisible by 24, 15, and 36, then it has to be divisible by 360. Greatest 6 digit number is 999999.
Common multiplies of 24, 15, 36 with 6 digits are 103680, 116640, 115520, …, 933120, 999720 with six digits.
∴ The greatest number consisting of 6 digits which is exactly divisible by 24, 15, 36 is 999720.
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
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.\[\frac{13}{125}\]
State Fundamental Theorem of Arithmetic.
Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
If two positive integers A and B can be expressed as A = xy3 and B = xiy2z; x, y being prime numbers, the LCM (A, B) is ______.
For some integer q, every odd integer is of the form ______.
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.
Explain why 3 × 5 × 7 + 7 is a composite number.
(HCF × LCM) for the numbers 30 and 70 is ______.
