NCERT Solutions for Class 5th Maths Chapter 13 A spider jumps 3, a grasshopper jumps 6; then the multiples of 4 and 6 — Spider and Grasshopper
Book page 166 Updated on2026-09-19
Q1.
A spider takes a jump of 3 every time. A grasshopper takes a jump of 6 each time. Use the number line to find the common multiples of 3 and 6.Page 166 — the number line. Both start at 0. The spider’s first jump is shown in green and the grasshopper’s first jump in purple.
Answer
They land together on 6, 12, 18, 24 … — that is, on every multiple of 6.
The spider touches 3, 6, 9, 12, 15, 18. The grasshopper touches 6, 12, 18. Every grasshopper spot is also a spider spot.
Why it happens: The grasshopper's jump of 6 is exactly two of the spider's jumps of 3. So wherever the grasshopper lands, the spider has just landed too. That is why every single grasshopper spot is shared.
Tip: Here the first common multiple is 6 — the bigger of the two numbers. This always happens when one number is a multiple of the other.
Q2.
6 and 12 are two common multiples of 3 and 6. You can continue the pattern to find more common multiples. What do you notice about the common multiples of 3 and 6? Discuss.Page 166 — the number line. Both start at 0. The spider’s first jump is shown in green and the grasshopper’s first jump in purple.
Answer
Sample answer: The common multiples of 3 and 6 are 6, 12, 18, 24, 30, 36 … They are exactly the multiples of 6 — the grasshopper's own list. Nothing new has to be worked out, because 6 is already a multiple of 3.
What the class should notice:
The first common multiple is 6, which is the bigger of the two numbers.
The grasshopper's list is completely inside the spider's list. Every multiple of 6 is also a multiple of 3.
The pattern continues for ever — 36, 42, 48, 54, 60 …
Why it happens: 6 = 3 × 2. So a jump of 6 is just two jumps of 3 joined together. The grasshopper can never land anywhere the spider has not already been.
Compare with the last page: For 3 and 4 the first common multiple was 12 = 3 × 4. For 3 and 6 it is only 6, not 18. The difference is that 6 is a multiple of 3, while 4 is not.
Q3.
Let us write the multiples of two numbers — 4 and 6. Multiples of 4: 4, 8, 12, 16, … Multiples of 6: 6, 12, 18, … 12 and 24 are two of the common multiples of 4 and 6. List a few more.
Answer
A few more common multiples of 4 and 6 are 36, 48, 60, 72 and 84.
Why it happens: 4 and 6 both divide 12 exactly, and 12 is the smallest number they both divide. So every common multiple is a step of 12 along the number line.