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:
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 the sum of the exponents of prime factors in the prime factorization of 98.
If 13824 = 2a × 3b then find a and b
Three farmers have 490 kg, 588 kg and 882 kg of wheat respectively. Find the maximum capacity of a bag so that the wheat can be packed in exact number of bags.
The largest number which divides 60 and 75, leaving remainders 8 and 10 respectively, is ______.
The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.
The prime factorisation of the number 2304 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?
