Worked examples
Numbers just below 100
98 × 97
Deficits from 100: -2 and -3. Left part = 98-3 (or 97-2) = 95. Right part = 2×3 = 06. → 9506.
98 × 97 = 9506
96 × 93
-4 and -7. Left = 96-7 = 89. Right = 4×7 = 28. → 8928.
96 × 93 = 8928
89 × 98
-11 and -2. Left = 89-2 = 87. Right = 11×2 = 22. → 8722.
89 × 98 = 8722
Common mistakes
Watch the right-hand block
- Right part must have as many digits as the base has zeros. Base 100 → always 2 digits, so 2×3 is written 06, not 6.
- Carry when the right part overflows. If the product of deficits is 100 or more, carry into the left part.
- Cross-subtract consistently: 98-3 and 97-2 give the same left part — use it as a check.
Practice — your turn
Multiply using Nikhilam (base 100)
Each number is close to 100.
- 98 × 97
- 96 × 93
- 89 × 98
- 94 × 96
- 88 × 97
- 99 × 95
- 92 × 91
- 97 × 90
- 95 × 95
- 87 × 99
Answer key: 98×97 = 9506 • 96×93 = 8928 • 89×98 = 8722 • 94×96 = 9024 • 88×97 = 8536 • 99×95 = 9405 • 92×91 = 8372 • 97×90 = 8730 • 95×95 = 9025 • 87×99 = 8613
More questions
Good to know
Does Nikhilam work for numbers above the base too?
Yes. For 103×104 use surpluses +3, +4: left = 103+4 = 107, right = 3×4 = 12 → 10712. The method mirrors the below-base case.
Which base should I choose?
Pick the nearest power of ten (10, 100, 1000). Numbers close to that base give the smallest deficits and the easiest arithmetic.
Vedic Maths — Veda Topper
Base Multiplication (Nikhilam) — Numbers Near 100
When two numbers sit close to a base like 100, you can multiply them almost instantly using the sutra Nikhilam Navatashcaramam Dashatah. Find how far each is from the base, cross-subtract, and multiply the little differences.
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The rule (numbers just below 100)
- Write how far each number is below 100 (its deficit).
- Left part = one number minus the other number's deficit (both ways give the same answer).
- Right part = the two deficits multiplied (write it as 2 digits).
Example 1 — 97 × 96
Deficits: 100−97 = 3, 100−96 = 4
Left: 97 − 4 = 93 (or 96 − 3 = 93)
Right: 3 × 4 = 12
Join: 93 | 12
97 × 96 = 9312
Example 2 — 98 × 88
Deficits: 2 and 12
Left: 98 − 12 = 86
Right: 2 × 12 = 24
Join: 86 | 24
98 × 88 = 8624
Example 3 (carry) — 88 × 88
Deficits: 12 and 12
Left: 88 − 12 = 76
Right: 12 × 12 = 144 → keep 44, carry 1
Left becomes 76 + 1 = 77
88 × 88 = 7744
Above the base
For numbers just above 100, use surpluses instead, and add the cross figure.
Example 4 — 103 × 104
Surpluses: 3 and 4
Left: 103 + 4 = 107
Right: 3 × 4 = 12
Join: 107 | 12
103 × 104 = 10712
Why it works
Writing the numbers as (100−a) and (100−b), their product is 100(100−a−b) + ab. The bracket is the "cross-subtract" step, and ab is the product of the deficits.
Practice (answers below):
1) 96 × 93 2) 99 × 97 3) 94 × 92 4) 102 × 106 5) 89 × 99
Answers: 1) 8928 2) 9603 3) 8648 4) 10812 5) 8811
1) 96 × 93 2) 99 × 97 3) 94 × 92 4) 102 × 106 5) 89 × 99
Answers: 1) 8928 2) 9603 3) 8648 4) 10812 5) 8811
More Vedic Maths tricks
← Vedic Maths home Multiply by 11 in one lineSquare numbers ending in 5Vertically & crosswiseSquares near a base (Yavadunam)Instant division by 9Subtraction: all from 9All 16 Sutras & 13 sub-sutras
Frequently asked questions
What is Nikhilam multiplication in Vedic Maths?
Nikhilam ("all from 9 and the last from 10") multiplies numbers near a base like 100 by using how far each is from the base: cross-subtract for the left part and multiply the differences for the right part.
Can Nikhilam multiply numbers above 100?
Yes. Use the surplus (how far above the base) and add the cross figure instead of subtracting. 103 × 104 = 10712.
When is base multiplication most useful?
When both numbers are close to 10, 100 or 1000 — such as 97 × 96 or 108 × 106 — where it is far faster than long multiplication.
Learn all of this live. Veda Topper runs online Vedic Maths classes for kids and adults, worldwide. Book a free demo class → · WhatsApp us →