Dell Inc. agreed to buy EMC Corp. for about $67 billion in the largest technology acquisition ever as Michael Dell looks to leverage EMC’s dominance in storage devices amid intensifying competition.

The computer maker plans to pay $24.05 a share in cash plus tracking stock in EMC’s prize holding, software maker VMware Inc., valued at about $9 for each EMC share. EMC’s stock climbed 1.8 percent Monday to $28.35. Dell will add almost $50 billion to its debt load to complete the purchase, people familiar with the matter said, on top of the $11 billion it already is carrying.

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