Question

Using fundamental theorem of arithmetic find LCM and HCF:questions (a) 408 and 170

Answer 1

(i) Since, 26 = 2 × 13 and, 91 = 7 × 13



∴ L.C.M. = Product of each prime factor with highest powers = 2 × 13 × 7 = 182. (Answer)
i.e., L.C.M. (26, 91) = 182. (Answer)
H.C.F. = Product of common prime factors with lowest powers. = 13.
i.e., H.C.F (26, 91) = 13.

(ii) Since, 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 = 24 × 34 and, 2520 = 2 × 2 × 2 × 3 × 3 × 5 × 7 = 23 × 32 × 5 × 7

Answer 2

here is ur ans...

Using fundamental theorem of arithmetic..provided in pic.



using Euclid's division algorithm provided below..

408= 170 * 2 + 68

170 = 68 *2+ 34

68 = 34* 2 + 0

thus...h.c.f is 34..