If the HCF of two positive integers is 26. Then their LCM cannot be?

LCM of 5, 10, 15, 20, 25 and 30 is 300. So, the bell will toll together after every 300s (5min).
So, the number of times they toll together = 60/5 + 1=13

Required number = H.C.F of (1657 - 6) and (2037 - 5)
= H.C.F of 1651 and 2032
= 127

L.C.M of 5, 6 , 7, 8 is 840
So, the number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2

? Required number = (840 x 2 + 3 ) = 1683

L. C .M of 9, 11, 13 is 1287
On dividing 1294 by 1287, the remainder is 7 .

? 1 must be subtracted from 1294, so that 1293 when divided by 9, 11, 13 leaves in each case the same remainder 6 .

Since 2, 3, 7, 11 are prime numbers and the given expression is
2¹⁰ x 3¹⁰ x 7¹⁷ x 11²⁷

So the number of prime factors in the given expression is (10 + 10 + 17 + 27 ) = 64.

The HCF of m and n is 1, so m and n are prime number.
Let m = 7 and n = 5 ? m + n = 12
HCF of(m + n)and m = HCF of 12 and 7 = 1
Similarly, HCF of (m - n) and n = 1

Suppose two numbers are 3N and 5N.
Then, 3N x 5N = HCF x LCM
? 15N² = 16 x 240
? N² = 256
? N = 16
So, the number are 3N = 3 x 16 = 48 and 5N = 5 x 16 = 80.

Find HCF of x³ +c x² -x + 2c and x² + cx - 2 by long division method and get remainder
? Remainder = 2c - 2/c
Since,remainder should be zero
? 2c² - 2 = 0
? 2(c² -1) = 0 ? c= ± 1

The required greatest number is the HCF of (263 - 7, 935 - 7, 1383 - 7)
i.e., HCF of 256, 928 and 1376 = 32

The HCF of [(480 - 390), (620 - 480), (620 - 390)]
= HCF of 90, 140, 230 = 10