Three Digit Multiplication Shortcut

1) 123*456 

I II III

1 2 3            

4 5 6  

• Multiply column III. Here, it's 18. Write 8 and carry over 1.  Result=>__8
• Cross multiply column II and III diagonally. ie 2*6 and 3*5. We get 12 and 15 respectively. Add both, you'll get 27. Add the carry over from previous step. So 28 is what we get. Write 8 and carry over 2. Result=>__88
• Now we need to cross multiply I and III diagonally like the previous step and multiply column II. Add up all the three numbers. 1*6+3*4+2*5=28+2(carry over from previous step)=30. Write 0 and carry over 3. Result=>__088
• Now cross multiply I and II and add the resultant numbers. 1*5+2*4=13+3(carry)=16. Write 6 and carry over 1. Result=>__6088
• Finally, multiply column I. 1*4=4+1(carry)=5 Result=>56088

2) 123*456

I came up with this one myself. lol I find this easier than the vedic math shortcut above.

hundreds tens ones

100           20          3

400           50           6

• I've just written the place value of each digit.
• Take 100 and multiply with all three places of the second number. (100*400=40000)+(100*50=5000)+(100*6=600)=45600
• Take 20 and repeat. (20*400=8000)+(20*50=1000)+(20*6=120)=9120
• Take 3 and repeat. (3*400=1200)+(3*50=150)+(3*6=18)=1368
• Add all three results=> 45600+9120+1368=56088.