Asked by ashokkushwaha12 | 21st Apr, 2015, 09:42: AM

Expert Answer:

To find LCM or HCF of two or more than two numbers, we write them in prime factorised form.
3240 equals 2 cubed cross times 3 to the power of 4 cross times 5...... left parenthesis 1 right parenthesis 3600 equals 2 to the power of 4 cross times 3 squared cross times 5 squared...... left parenthesis 2 right parenthesis F i r s t space f i n d space t h e space L C M space o f space t h e s e space t w o space n u m b e r s. space T o space f i n d space L C M space comma space w e space t a k e space h i g h e s t space p o w e r s space o f space e a c h space p r i m e space n u m b e r space f r o m space t h e space g i v e n space t w o space n u m b e r s. H e n c e comma space L C M space o f space a b o v e space t w o space n u m b e r s equals 2 to the power of 4 cross times 3 to the power of 4 cross times 5 squared..... left parenthesis 3 right parenthesis S i n c e comma space t h e space p o w e r space o f space apostrophe 2 apostrophe space i n space 3600 space i s space apostrophe 4 apostrophe comma space t h e space L C M space w i l l space h a v e space a t l e a s t space p o w e r space o f space apostrophe 2 apostrophe space a s space apostrophe 4 apostrophe. space S o comma space a s s u m i n g space t h a t space t h e space q u e s t i o n space s t a t e s space t h a t space t h e space L C M space i s space 2 to the power of 4 cross times 3 to the power of 5 cross times 5 squared cross times 7 squared space f o r space t h r e e space n u m b e r s comma space w e space s o l v e space t h e space p r o b l e m. A l s o space g i v e n space t h a t space H C F space equals space 36 equals 2 squared cross times 3 squared...... left parenthesis 4 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space t h e space g i v e n space t w o space n u m b e r s space h a v e space p o w e r s space o f space apostrophe 2 apostrophe space a s space apostrophe 3 apostrophe space a n d space apostrophe 4 apostrophe. H e n c e comma space i f space H C F space h a s space 2 squared comma space t h e n space t h e space t h i r d space n u m b e r space s h o u l d space h a v e space 2 squared space i n space i t........ left parenthesis 5 right parenthesis S i m i l a r l y comma space c o n s i d e r i n g space t h e space p o w e r s space o f space apostrophe 3 apostrophe comma space L C M thin space h a s space p o w e r space apostrophe 5 apostrophe space a n d space H C F space h a s space p o w e r space a s space apostrophe 2 apostrophe. space S i n c e space w e space a l r e a d y space h a v e space 3 squared space i n space 3600 comma space t h e space H C F space c o n d i t i o n space i s space a l r e a d y space s a t i s f i e d. space B u t comma space f o r space t h e space L C M space t o space h a v e space 3 to the power of 5 comma space t h e space t h i r d space n u m b e r space m u s t space h a v e space 3 to the power of 5........ left parenthesis 6 right parenthesis space left parenthesis sin c e space t h e space o t h e r space t w o space n u m b e r s space d o space n o t space h a v e space p o w e r space o f space apostrophe 3 apostrophe space a s space apostrophe 5 apostrophe right parenthesis A l s o comma space sin c e space t h e space H C F space d o e s space n o t space h a v e space a n y space p o w e r space o f space apostrophe 5 apostrophe comma space t h e space t h i r d space n u m b e r space a l s o space s h o u l d space n o t space h a v e space a n y space p o w e r space o f space apostrophe 5 apostrophe..... left parenthesis 7 right parenthesis left parenthesis sin c e space t h e space o t h e r space t w o space n u m b e r s space a l r e a d y space h a v e space p o w e r s space o f space apostrophe 5 apostrophe right parenthesis F i n a l l y space t h e space L C M space h a s space 7 squared space i n space i t. space N o n e space o f space t h e space o t h e r space t w o space n u m b e r s space h a v e space 7 space a s space f a c t o r. space H e n c e comma space t h e space t h i r d space n u m b e r space s h o u l d space h a v e space 7 squared space i n space i t.... left parenthesis 8 right parenthesis S o space f r o m space left parenthesis 5 right parenthesis comma space left parenthesis 6 right parenthesis comma space left parenthesis 7 right parenthesis space a n d space left parenthesis 8 right parenthesis space w e space g e t space t h e space t h i r d space n u m b e r space i s space 2 squared cross times 3 to the power of 5 cross times 7 squared equals 47628

Answered by satyajit samal | 21st Apr, 2015, 10:42: AM